Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #27133073 | C2 | semidirect |
| 4. #27133072 | C2 | semidirect |
| 5. #27133069 | C2 | semidirect |
| 6. #27133067 | C2 | semidirect |
| 7. #27133060 | C2 | semidirect |
| 11. #501×C191 | C2 | semidirect |
| 52. #15690270 | Q8 | semidirect |
| 95. C191⋊C8 | C2×Q8 | semidirect |
| 103. C8×C191 | C2×Q8 | semidirect |
| 124. C191 | #3165 | semidirect |
| 131. #501 | D191 | semidirect |
| 228. C8 | Q8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133219 | 2 |
| C4⋊Q8×D191 | 2 |
| #27133073 | 2 |
| #27133072 | 2 |
| #27133069 | 2 |
| #27133067 | 2 |
| #27133060 | 2 |
| #27132704 | 2 |
| #27132702 | 2 |
| #27132615 | 2 |
| #501×C191 | 2 |
| #3165 | 191 |