Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20259342 | C2 | semidirect |
| 2. #27133213 | C2 | semidirect |
| 3. #27133045 | C2 | semidirect |
| 4. #27133042 | C2 | semidirect |
| 5. #27133039 | C2 | semidirect |
| 6. #27133037 | C2 | semidirect |
| 7. #27133035 | C2 | semidirect |
| 8. C2×C4×C191⋊C8 | C2 | semidirect |
| 9. #532×C191 | C2 | semidirect |
| 42. C2×C191⋊C8 | D4 | semidirect |
| 93. C4×C191 | #135 | semidirect |
| 101. C191 | #3147 | semidirect |
| 105. #532 | D191 | semidirect |
| 196. C4 | #20259342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259342 | 2 |
| #27133213 | 2 |
| #27133045 | 2 |
| #27133042 | 2 |
| #27133039 | 2 |
| #27133037 | 2 |
| #27133035 | 2 |
| C2×C4×C191⋊C8 | 2 |
| #532×C191 | 2 |
| #3147 | 191 |