Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #126×C379 | C2 |
| prime radical | #27131304 | C2 |
| hypercenter | #126 | D379 |
| hypocenter | C379 | #529 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131325 | C2 | semidirect |
| 2. #27131321 | C2 | semidirect |
| 3. #27131317 | C2 | semidirect |
| 4. #27131316 | C2 | semidirect |
| 5. #27131313 | C2 | semidirect |
| 6. #27131309 | C2 | semidirect |
| 8. #27131296 | C2 | semidirect |
| 9. #27131293 | C2 | semidirect |
| 10. (C22⋊D379)⋊C4 | C2 | semidirect |
| 11. (C22⋊D379)⋊C4 | C2 | semidirect |
| 12. #27131289 | C2 | semidirect |
| 13. #27131287 | C2 | semidirect |
| 14. C42×D379 | C2 | semidirect |
| 15. #126×C379 | C2 | semidirect |
| 103. C379 | #529 | semidirect |
| 106. #126 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131325 | 2 |
| #27131321 | 2 |
| #27131317 | 2 |
| #27131316 | 2 |
| #27131313 | 2 |
| #27131309 | 2 |
| #27131304 | 2 |
| #27131296 | 2 |
| #27131293 | 2 |
| (C22⋊D379)⋊C4 | 2 |
| #27131289 | 2 |
| #27131287 | 2 |
| C42×D379 | 2 |
| #126×C379 | 2 |
| #529 | 379 |