Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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×D379 |
| commutator, socle, cosocle | C22×C379 | C24 |
| Fitting, prime radical | #121×C379 | C2 |
| hypercenter | #121 | D379 |
| hypocenter | C379 | #529 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131324 | C2 | semidirect |
| 2. #27131322 | C2 | semidirect |
| 3. #27131318 | C2 | semidirect |
| 4. #27131312 | C2 | semidirect |
| 5. #27131310 | C2 | semidirect |
| 6. #27131296 | C2 | semidirect |
| 7. D4×Dic379 | C2 | semidirect |
| 8. D4×Dic379 | C2 | semidirect |
| 9. #27131287 | C2 | semidirect |
| 10. C2×C4×Dic379 | C2 | semidirect |
| 74. C379 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131324 | 2 |
| #27131322 | 2 |
| #27131318 | 2 |
| #27131312 | 2 |
| #27131310 | 2 |
| #27131296 | 2 |
| D4×Dic379 | 2 |
| #27131287 | 2 |
| C2×C4×Dic379 | 2 |
| #121×C379 | 2 |
| #529 | 379 |