Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | #117×C431 | C2 |
| hypercenter | #117 | D431 |
| hypocenter | C431 | #535 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20293800 | C2 | semidirect |
| 2. C22×D1724 | C2 | semidirect |
| 3. #28352186 | C2 | semidirect |
| 4. #28352177 | C2 | semidirect |
| 5. #28352164 | C2 | semidirect |
| 6. #28352159 | C2 | semidirect |
| 7. #117×C431 | C2 | semidirect |
| 10. C2×Dic862 | C22 | semidirect |
| 14. C2×D1724 | C22 | semidirect |
| 15. C2×D1724 | C22 | semidirect |
| 17. C2×C4×D431 | C22 | semidirect |
| 18. (C2×D431)⋊C4 | C22 | semidirect |
| 20. C4⋊C4×C431 | C22 | semidirect |
| 22. C42×C431 | C22 | semidirect |
| 36. C2×C4×C431 | D4 | semidirect |
| 57. C431 | #535 | semidirect |
| 65. #117 | D431 | semidirect |
| 77. C4⋊C4 | C2×D431 | semidirect |
| 80. C42 | C2×D431 | semidirect |
| 94. C2×C4 | D1724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293800 | 2 |
| C22×D1724 | 2 |
| #28352186 | 2 |
| #28352177 | 2 |
| #28352164 | 2 |
| #28352159 | 2 |
| #117×C431 | 2 |
| #535 | 431 |