Finite Group DatabasebetaFinite Group DatabasebetaOrder 14694.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C79×C31⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D2449 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C31×C79 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×D79 | — | 31 | 1 | no | maximal, Hall |
| 5 | C3×C79 | — | 31 | 1 | no | Hall |
| 6 | D31⋊C3 | — | 79 | 1 | no | maximal, Hall |
| 7 | D79 | — | 93 | 1 | no | Hall |
| 8 | C31⋊C3 | D79 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C79 | D31⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | D31 | — | 79 | 1 | no | Hall |
| 11 | C31 | C3×D79 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C3 | — | 2449 | 1 | no | Hall |
| 13 | C3 | — | 31 | 1 | no | Sylow |
| 14 | C2 | — | 7347 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C79 | C2×C3 |
| LCS | G ▷ C31×C79 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×C31⋊C3 | C2 | semidirect |
| 2. D2449 | C3 | semidirect |
| 3. C31×C79 | C2×C3 | semidirect |
| 8. C31⋊C3 | D79 | semidirect |
| 9. C79 | D31⋊C3 | semidirect |
| 11. C31 | C3×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×C31⋊C3 | 2 |
| D2449 | 3 |
| C3×D79 | 31 |
| D31⋊C3 | 79 |