Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133291 | C2 | semidirect |
| 3. #27132971 | C2 | semidirect |
| 4. #27132964 | C2 | semidirect |
| 5. #27132954 | C2 | semidirect |
| 6. #27132949 | C2 | semidirect |
| 7. #27132705 | C2 | semidirect |
| 8. C2×#20259254 | C2 | semidirect |
| 11. #424×C191 | C2 | semidirect |
| 42. #15690287 | Q8 | semidirect |
| 123. C191 | #3084 | semidirect |
| 133. #424 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133143 | 2 |
| #27132971 | 2 |
| #27132964 | 2 |
| #27132954 | 2 |
| #27132949 | 2 |
| #27132705 | 2 |
| C2×#20259254 | 2 |
| #27132665 | 2 |
| #27132660 | 2 |
| #424×C191 | 2 |
| #3084 | 191 |