Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #27133001 | C2 | semidirect |
| 3. #27132987 | C2 | semidirect |
| 4. #27132911 | C2 | semidirect |
| 5. #27132894 | C2 | semidirect |
| 6. #27132813 | C2 | semidirect |
| 7. #27132802 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 9. #536×C191 | C2 | semidirect |
| 13. C2×#15690271 | C22 | semidirect |
| 14. C22×C191⋊C8 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259253 | C22 | semidirect |
| 24. #20259246 | C22 | semidirect |
| 25. #20259246 | C22 | semidirect |
| 29. C22⋊(C191⋊C8) | C22 | semidirect |
| 31. C22×Q8×C191 | C22 | semidirect |
| 37. C22⋊Q8×C191 | C22 | semidirect |
| 38. #117×C191 | C22 | semidirect |
| 137. C191 | #3200 | semidirect |
| 139. #536 | D191 | semidirect |
| 149. C22×Q8 | C2×D191 | semidirect |
| 162. C22⋊Q8 | C2×D191 | semidirect |
| 168. #117 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133227 | 2 |
| #27133001 | 2 |
| #27132987 | 2 |
| #27132911 | 2 |
| #27132894 | 2 |
| #27132813 | 2 |
| #27132802 | 2 |
| #27132630 | 2 |
| #536×C191 | 2 |
| #3200 | 191 |