Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #27133218 | C2 | semidirect |
| 3. #27132962 | C2 | semidirect |
| 4. #27132961 | C2 | semidirect |
| 5. #27132950 | C2 | semidirect |
| 6. #27132944 | C2 | semidirect |
| 7. #27132943 | C2 | semidirect |
| 8. #27132702 | C2 | semidirect |
| 9. #27132685 | C2 | semidirect |
| 11. #476×C191 | C2 | semidirect |
| 15. #20259322 | C22 | semidirect |
| 16. #20259313 | C22 | semidirect |
| 30. #20259256 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. C4⋊(C191⋊C8) | C22 | semidirect |
| 34. Dic191⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C191 | C22 | semidirect |
| 40. #106×C191 | C22 | semidirect |
| 41. C4⋊C8×C191 | C22 | semidirect |
| 48. D4×D191 | Q8 | semidirect |
| 144. C191 | #3077 | semidirect |
| 151. #476 | D191 | semidirect |
| 161. C4⋊Q8 | C2×D191 | semidirect |
| 180. #106 | C2×D191 | semidirect |
| 183. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| C4×D4×D191 | 2 |
| #27132962 | 2 |
| #27132961 | 2 |
| #27132950 | 2 |
| #27132944 | 2 |
| #27132943 | 2 |
| #27132702 | 2 |
| #27132685 | 2 |
| #27132666 | 2 |
| #476×C191 | 2 |
| #3077 | 191 |