Finite Group DatabasebetaFinite Group DatabasebetaOrder 12393.
116 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C9×C17×C27 | C3 | 1 | 3 | yes | maximal |
| 2 | C9×C17×C27 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×C17×C27 | C9 | 1 | 9 | yes | — |
| 4 | C3×C17×C27 | C9 | 1 | 3 | yes | — |
| 5 | C92×C17 | C32 | 1 | 1 | yes | characteristic |
| 6 | #10624443 | C17 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 7 | C3×C9×C17 | C3×C9 | 1 | 1 | yes | characteristic |
| 8 | C3×C9×C17 | C3×C9 | 1 | 3 | yes | — |
| 9 | C17×C27 | — | 3 | 9 | no | — |
| 10 | C17×C27 | C27 | 1 | 9 | yes | complemented |
| 11 | C9×C27 | C3×C17 | 1 | 3 | yes | — |
| 12 | C9×C27 | C3×C17 | 1 | 1 | yes | characteristic |
| 13 | C32×C17 | C92 | 1 | 1 | yes | characteristic |
| 14 | C9×C17 | C3×C27 | 1 | 3 | yes | — |
| 15 | C9×C17 | C27⋊C3 | 1 | 9 | yes | — |
| 16 | C3×C27 | C9×C17 | 1 | 9 | yes | — |
| 17 | C3×C27 | C9×C17 | 1 | 3 | yes | — |
| 18 | C92 | C32×C17 | 1 | 1 | yes | characteristic |
| 19 | C3×C17 | C9×C27 | 1 | 1 | yes | characteristic |
| 20 | C3×C17 | #6864 | 1 | 3 | yes | — |
| 21 | C3×C9 | C3×C9×C17 | 1 | 1 | yes | characteristic |
| 22 | C3×C9 | C3×C9×C17 | 1 | 3 | yes | — |
| 23 | C27 | — | 3 | 9 | no | — |
| 24 | C27 | C17×C27 | 1 | 9 | yes | complemented |
| 25 | C17 | #10624443 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 26 | C32 | C92×C17 | 1 | 1 | yes | characteristic |
| 27 | C9 | C3×C17×C27 | 1 | 3 | yes | — |
| 28 | C9 | C17×C27⋊C3 | 1 | 9 | yes | — |
| 29 | C3 | C9×C17×C27 | 1 | 1 | yes | characteristic |
| 30 | C3 | C17×#6864 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C92×C17 | C32 |
| commutator | C3 | C9×C17×C27 |
| Frattini, cosocle | C92 | C32×C17 |
| socle, prime radical | C32×C17 | C92 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C92×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #10624443 | C17 | direct (N × H) |
| 10. C17×C27 | C27 | semidirect |
| 24. C27 | C17×C27 | semidirect |
| 25. C17 | #10624443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C17×C27 | 3 |
| #10624443 | 17 |