Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #123×C379 | C2 |
| prime radical | #27131303 | C2 |
| hypercenter | #123 | D379 |
| hypocenter | C379 | #529 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131326 | C2 | semidirect |
| 2. #27131324 | C2 | semidirect |
| 3. #27131321 | C2 | semidirect |
| 4. #27131317 | C2 | semidirect |
| 5. #27131314 | C2 | semidirect |
| 6. #27131308 | C2 | semidirect |
| 8. #27131296 | C2 | semidirect |
| 9. D4×Dic379 | C2 | semidirect |
| 10. (C22⋊D379)⋊C4 | C2 | semidirect |
| 11. (C22⋊D379)⋊C4 | C2 | semidirect |
| 12. #27131289 | C2 | semidirect |
| 13. #27131287 | C2 | semidirect |
| 14. C2×C4×Dic379 | C2 | semidirect |
| 15. #123×C379 | C2 | semidirect |
| 103. C379 | #529 | semidirect |
| 110. #123 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131326 | 2 |
| #27131324 | 2 |
| #27131321 | 2 |
| #27131317 | 2 |
| #27131314 | 2 |
| #27131308 | 2 |
| #27131303 | 2 |
| #27131296 | 2 |
| D4×Dic379 | 2 |
| (C22⋊D379)⋊C4 | 2 |
| #27131289 | 2 |
| #27131287 | 2 |
| C2×C4×Dic379 | 2 |
| #123×C379 | 2 |
| #529 | 379 |