Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131376 | C2 | semidirect |
| 2. #27131357 | C2 | semidirect |
| 3. #27131355 | C2 | semidirect |
| 4. #27131353 | C2 | semidirect |
| 5. #27131350 | C2 | semidirect |
| 6. D8×D379 | C2 | semidirect |
| 7. #27131337 | C2 | semidirect |
| 8. C2×D8×C379 | C2 | semidirect |
| 10. #20258606 | C22 | semidirect |
| 12. #20258605 | C22 | semidirect |
| 15. D4×D379 | C22 | semidirect |
| 16. Dic1516 | C22 | semidirect |
| 17. #20258595 | C22 | semidirect |
| 18. #20258594 | C22 | semidirect |
| 19. D3032 | C22 | semidirect |
| 20. #20258591 | C22 | semidirect |
| 21. #20258590 | C22 | semidirect |
| 22. #20258589 | C22 | semidirect |
| 23. C8×D379 | C22 | semidirect |
| 24. C2×D4×C379 | C22 | semidirect |
| 25. D8×C379 | C22 | semidirect |
| 26. D8×C379 | C22 | semidirect |
| 27. C2×C8×C379 | C22 | semidirect |
| 62. C379 | #576 | semidirect |
| 70. C2×D8 | D379 | semidirect |
| 79. C2×D4 | C2×D379 | semidirect |
| 85. D8 | C2×D379 | semidirect |
| 86. D8 | C2×D379 | semidirect |
| 90. C2×C8 | C2×D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131376 | 2 |
| #27131357 | 2 |
| #27131355 | 2 |
| #27131353 | 2 |
| #27131350 | 2 |
| D8×D379 | 2 |
| #27131337 | 2 |
| C2×D8×C379 | 2 |
| #576 | 379 |