Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27132973 | C2 | semidirect |
| 4. #27132969 | C2 | semidirect |
| 5. #27132957 | C2 | semidirect |
| 6. #27132947 | C2 | semidirect |
| 44. C2×Dic382 | Q8 | semidirect |
| 116. C191 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133140 | 2 |
| #27132973 | 2 |
| #27132969 | 2 |
| #27132957 | 2 |
| #27132947 | 2 |
| #27132706 | 2 |
| #27132689 | 2 |
| #27132671 | 2 |
| C2×#20259247 | 2 |
| #427×C191 | 2 |
| #3082 | 191 |