Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#20259352 | C2 | semidirect |
| 2. C22×#15690275 | C2 | semidirect |
| 3. #27133234 | C2 | semidirect |
| 4. #27132825 | C2 | semidirect |
| 5. #27132814 | C2 | semidirect |
| 6. #27132668 | C2 | semidirect |
| 7. #27132659 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 10. C22×Dic382 | C22 | semidirect |
| 12. C2×#15690277 | C22 | semidirect |
| 14. C2×#15690275 | C22 | semidirect |
| 15. C2×#15690275 | C22 | semidirect |
| 16. C2×#15690271 | C22 | semidirect |
| 17. C22×C191⋊C8 | C22 | semidirect |
| 21. #20259301 | C22 | semidirect |
| 22. #20259281 | C22 | semidirect |
| 23. #20259246 | C22 | semidirect |
| 24. #20259243 | C22 | semidirect |
| 25. #20259243 | C22 | semidirect |
| 26. C22⋊(C191⋊C8) | C22 | semidirect |
| 146. C191 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C22×#15690275 | 2 |
| #27133234 | 2 |
| #27132825 | 2 |
| #27132814 | 2 |
| #27132668 | 2 |
| #27132659 | 2 |
| #27132630 | 2 |
| C2×H(5,𝔽2)×C191 | 2 |
| #3009 | 191 |