Finite Group DatabasebetaFinite Group DatabasebetaOrder 18348.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×C11×C139 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C11×Dic139 | — | 3 | 1 | no | maximal, Hall |
| 3 | C3×C11×C139 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C11×C139 | D3 | 1 | 1 | yes | characteristic |
| 5 | Dic417 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C11×C139 | Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C2×C3×C139 | C2×C11 | 1 | 1 | yes | characteristic |
| 8 | Dic139 | — | 3 | 1 | no | Hall |
| 9 | C3×C139 | C4×C11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | C2×C139 | D3×C11 | 1 | 1 | yes | characteristic |
| 11 | C139 | C11×Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C11×Dic3 | — | 139 | 1 | no | maximal, Hall |
| 13 | C2×C3×C11 | D139 | 1 | 1 | yes | characteristic |
| 14 | C4×C11 | — | 417 | 1 | no | Hall |
| 15 | C3×C11 | Dic139 | 1 | 1 | yes | characteristic, complemented, Hall |
| 16 | C2×C11 | D417 | 1 | 1 | yes | characteristic |
| 17 | Dic3 | — | 139 | 1 | no | Hall |
| 18 | C11 | Dic417 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 19 | C2×C3 | C11×D139 | 1 | 1 | yes | characteristic |
| 20 | C4 | — | 417 | 1 | no | Sylow |
| 21 | C3 | C11×Dic139 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 22 | C2 | C11×D417 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D417 |
| commutator, hypocenter | C3×C139 | C4×C11 |
| Frattini | C2 | C11×D417 |
| Fitting, socle, prime radical | C2×C3×C11×C139 | C2 |
| cosocle | C2×C3×C139 | C2×C11 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 ◁ C2×C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C11×C139 | C4 | semidirect |
| 5. Dic417 | C11 | direct (N × H) |
| 6. C11×C139 | Dic3 | semidirect |
| 9. C3×C139 | C4×C11 | semidirect |
| 11. C139 | C11×Dic3 | semidirect |
| 15. C3×C11 | Dic139 | semidirect |
| 18. C11 | Dic417 | direct (N × H) |
| 21. C3 | C11×Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C11×C139 | 2 |
| C11×Dic139 | 3 |
| Dic417 | 11 |
| C11×Dic3 | 139 |