Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Fitting | C4×Q8×C389 | C2 |
| prime radical | C22×D389 | C23 |
| hypercenter | C4×Q8 | D389 |
| hypocenter | C389 | #541 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27159382 | C2 | semidirect |
| 4. #27159376 | C2 | semidirect |
| 5. #27159375 | C2 | semidirect |
| 6. #27159374 | C2 | semidirect |
| 9. C4×Dic778 | C2 | semidirect |
| 11. C4×Q8×C389 | C2 | semidirect |
| 67. C389 | #541 | semidirect |
| 78. C4×Q8 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159382 | 2 |
| #27159379 | 2 |
| #27159378 | 2 |
| #27159376 | 2 |
| #27159375 | 2 |
| #27159374 | 2 |
| #27159364 | 2 |
| #27159360 | 2 |
| C4×Dic778 | 2 |
| #27159341 | 2 |
| C4×Q8×C389 | 2 |
| #541 | 389 |