Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131378 | C2 | semidirect |
| 2. #27131377 | C2 | semidirect |
| 3. #27131364 | C2 | semidirect |
| 4. #27131359 | C2 | semidirect |
| 5. #27131353 | C2 | semidirect |
| 6. C2×#20258595 | C2 | semidirect |
| 7. #131×C379 | C2 | semidirect |
| 10. #20258606 | C22 | semidirect |
| 12. C2×Dic758 | C22 | semidirect |
| 16. Dic1516 | C22 | semidirect |
| 17. #20258595 | C22 | semidirect |
| 18. #20258595 | C22 | semidirect |
| 19. #20258595 | C22 | semidirect |
| 20. D3032 | C22 | semidirect |
| 22. M16×C379 | C22 | semidirect |
| 23. C2×C8×C379 | C22 | semidirect |
| 53. C379 | #577 | semidirect |
| 61. #131 | D379 | semidirect |
| 76. M16 | C2×D379 | semidirect |
| 77. C2×C8 | C2×D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131378 | 2 |
| #27131377 | 2 |
| #27131364 | 2 |
| #27131359 | 2 |
| #27131353 | 2 |
| C2×#20258595 | 2 |
| #131×C379 | 2 |
| #577 | 379 |