Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 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. #27132973 | C2 | semidirect |
| 4. #27132965 | C2 | semidirect |
| 5. #27132955 | C2 | semidirect |
| 6. #27132949 | C2 | semidirect |
| 7. #27132943 | C2 | semidirect |
| 8. #27132698 | C2 | semidirect |
| 9. C4⋊C8×D191 | C2 | semidirect |
| 11. #476×C191 | C2 | semidirect |
| 44. #15690286 | Q8 | semidirect |
| 134. C191 | #3076 | semidirect |
| 141. #476 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| C4×#15690286 | 2 |
| #27132973 | 2 |
| #27132965 | 2 |
| #27132955 | 2 |
| #27132949 | 2 |
| #27132943 | 2 |
| #27132698 | 2 |
| C4⋊C8×D191 | 2 |
| #27132656 | 2 |
| #476×C191 | 2 |
| #3076 | 191 |