Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #127×C389 | C2 |
| hypercenter | #127 | D389 |
| hypocenter | C389 | #550 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20261965 | C2 | semidirect |
| 2. #27159380 | C2 | semidirect |
| 3. #27159356 | C2 | semidirect |
| 4. #27159355 | C2 | semidirect |
| 5. C4×Dic778 | C2 | semidirect |
| 6. C4×D1556 | C2 | semidirect |
| 7. D4×Dic389 | C2 | semidirect |
| 8. #127×C389 | C2 | semidirect |
| 27. Dic778 | D4 | semidirect |
| 52. C4×C389 | #41 | semidirect |
| 61. C389 | #550 | semidirect |
| 65. #127 | D389 | semidirect |
| 117. C4 | #20261965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261965 | 2 |
| #27159380 | 2 |
| #27159356 | 2 |
| #27159355 | 2 |
| C4×Dic778 | 2 |
| C4×D1556 | 2 |
| D4×Dic389 | 2 |
| #127×C389 | 2 |
| #550 | 389 |