Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #27133071 | C2 | semidirect |
| 4. #27133070 | C2 | semidirect |
| 5. #27133064 | C2 | semidirect |
| 6. #27133060 | C2 | semidirect |
| 44. C2×C191⋊C8 | Q8 | semidirect |
| 65. M16×C191 | Q8 | semidirect |
| 112. C191 | #3163 | semidirect |
| 159. M16 | Dic382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133294 | 2 |
| #27133291 | 2 |
| #27133071 | 2 |
| #27133070 | 2 |
| #27133064 | 2 |
| #27133060 | 2 |
| #27132705 | 2 |
| #27132699 | 2 |
| C2×#20259253 | 2 |
| #27132621 | 2 |
| #428×C191 | 2 |
| #3163 | 191 |