Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#20259346 | C2 | semidirect |
| 2. #27133308 | C2 | semidirect |
| 3. #27133047 | C2 | semidirect |
| 4. #27132910 | C2 | semidirect |
| 5. #27132878 | C2 | semidirect |
| 6. #27132826 | C2 | semidirect |
| 7. #27132798 | C2 | semidirect |
| 8. #27132742 | C2 | semidirect |
| 9. C4×D8×C191 | C2 | semidirect |
| 11. C2×D4×D191 | C22 | semidirect |
| 13. C2×Dic764 | C22 | semidirect |
| 14. C2×#15690276 | C22 | semidirect |
| 15. C2×#15690275 | C22 | semidirect |
| 18. C2×#15690270 | C22 | semidirect |
| 19. #20259310 | C22 | semidirect |
| 21. #20259302 | C22 | semidirect |
| 27. C4⋊(C191⋊C8) | C22 | semidirect |
| 28. #20259245 | C22 | semidirect |
| 29. #20259242 | C22 | semidirect |
| 30. (C2×D191)⋊C8 | C22 | semidirect |
| 32. C4×D4×C191 | C22 | semidirect |
| 33. #107×C191 | C22 | semidirect |
| 34. #102×C191 | C22 | semidirect |
| 35. C4×C8×C191 | C22 | semidirect |
| 65. D8×C191 | D4 | semidirect |
| 124. C191 | #3273 | semidirect |
| 133. C4×D8 | D191 | semidirect |
| 152. C4×D4 | C2×D191 | semidirect |
| 154. #107 | C2×D191 | semidirect |
| 158. #102 | C2×D191 | semidirect |
| 160. C4×C8 | C2×D191 | semidirect |
| 181. D8 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259346 | 2 |
| #27133308 | 2 |
| #27133047 | 2 |
| #27132910 | 2 |
| #27132878 | 2 |
| #27132826 | 2 |
| #27132798 | 2 |
| #27132742 | 2 |
| C4×D8×C191 | 2 |
| #3273 | 191 |