Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27133000 | C2 | semidirect |
| 4. #27132940 | C2 | semidirect |
| 5. #27132869 | C2 | semidirect |
| 6. #27132868 | C2 | semidirect |
| 8. #27132762 | C2 | semidirect |
| 9. #27132760 | C2 | semidirect |
| 10. #27132719 | C2 | semidirect |
| 11. #474×C191 | C2 | semidirect |
| 16. #20259322 | C22 | semidirect |
| 21. #20259287 | C22 | semidirect |
| 31. #20259255 | C22 | semidirect |
| 32. C4⋊(C191⋊C8) | C22 | semidirect |
| 33. #20259247 | C22 | semidirect |
| 34. #20259245 | C22 | semidirect |
| 37. #20259232 | C22 | semidirect |
| 38. C4⋊Q8×C191 | C22 | semidirect |
| 40. #107×C191 | C22 | semidirect |
| 41. C4⋊C8×C191 | C22 | semidirect |
| 146. C191 | #3110 | semidirect |
| 152. #474 | D191 | semidirect |
| 164. C4⋊Q8 | C2×D191 | semidirect |
| 181. #107 | 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 |
| #27133000 | 2 |
| #27132940 | 2 |
| #27132869 | 2 |
| #27132868 | 2 |
| #27132815 | 2 |
| #27132762 | 2 |
| #27132760 | 2 |
| #27132719 | 2 |
| #474×C191 | 2 |
| #3110 | 191 |