Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #121×C379 | C2 |
| hypercenter | #121 | D379 |
| hypocenter | C379 | #537 |
| 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. C2×#20258605 | C2 | semidirect |
| 2. #27131309 | C2 | semidirect |
| 3. #27131308 | C2 | semidirect |
| 4. #27131305 | C2 | semidirect |
| 5. #27131304 | C2 | semidirect |
| 6. #27131303 | C2 | semidirect |
| 7. #27131303 | C2 | semidirect |
| 8. C2×Dic379⋊C4 | C2 | semidirect |
| 9. #121×C379 | C2 | semidirect |
| 40. C2×Dic379 | D4 | semidirect |
| 75. C379 | #537 | semidirect |
| 84. #121 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258605 | 2 |
| #27131309 | 2 |
| #27131308 | 2 |
| #27131305 | 2 |
| #27131304 | 2 |
| #27131303 | 2 |
| C2×Dic379⋊C4 | 2 |
| #121×C379 | 2 |
| #537 | 379 |