Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15690272 | C2 | semidirect |
| 2. C2×#20259330 | C2 | semidirect |
| 3. #27133232 | C2 | semidirect |
| 4. #27133230 | C2 | semidirect |
| 5. #27132915 | C2 | semidirect |
| 6. #27132898 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132669 | C2 | semidirect |
| 9. #418×C191 | C2 | semidirect |
| 16. C2×#15690270 | C22 | semidirect |
| 18. C2×C8×D191 | C22 | semidirect |
| 23. #20259297 | C22 | semidirect |
| 24. #20259293 | C22 | semidirect |
| 28. #20259255 | C22 | semidirect |
| 29. #20259253 | C22 | semidirect |
| 30. #20259244 | C22 | semidirect |
| 34. #102×C191 | C22 | semidirect |
| 51. C2×C191⋊C8 | D4 | semidirect |
| 125. C191 | #3058 | semidirect |
| 135. #418 | D191 | semidirect |
| 160. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690272 | 2 |
| C2×#20259330 | 2 |
| #27133232 | 2 |
| #27133230 | 2 |
| #27132915 | 2 |
| #27132898 | 2 |
| #27132699 | 2 |
| #27132669 | 2 |
| #418×C191 | 2 |
| #3058 | 191 |