Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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. C2×#20259352 | C2 | semidirect |
| 2. C22×#15690276 | C2 | semidirect |
| 4. #27133140 | C2 | semidirect |
| 5. #27132888 | C2 | semidirect |
| 6. #27132862 | C2 | semidirect |
| 7. #27132689 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. #416×C191 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 16. C2×#15690275 | C22 | semidirect |
| 23. #20259287 | C22 | semidirect |
| 26. Dic191⋊C8 | C22 | semidirect |
| 31. #103×C191 | C22 | semidirect |
| 32. #102×C191 | C22 | semidirect |
| 36. C2×Dic382 | D4 | semidirect |
| 116. C191 | #3043 | semidirect |
| 126. #416 | D191 | semidirect |
| 147. #103 | C2×D191 | semidirect |
| 149. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| C22×#15690276 | 2 |
| #27133227 | 2 |
| #27133140 | 2 |
| #27132888 | 2 |
| #27132862 | 2 |
| #27132689 | 2 |
| #27132667 | 2 |
| #416×C191 | 2 |
| #3043 | 191 |