Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. C2×#20259344 | C2 | semidirect |
| 2. #27133241 | C2 | semidirect |
| 3. #27132921 | C2 | semidirect |
| 4. #27132916 | C2 | semidirect |
| 5. #27132892 | C2 | semidirect |
| 6. C2×#20259254 | C2 | semidirect |
| 7. #27132665 | C2 | semidirect |
| 8. C2×#131×C191 | C2 | semidirect |
| 56. C2×C8×C191 | D4 | semidirect |
| 105. C191 | #3060 | semidirect |
| 108. C2×#131 | D191 | semidirect |
| 157. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259344 | 2 |
| #27133241 | 2 |
| #27132921 | 2 |
| #27132916 | 2 |
| #27132892 | 2 |
| C2×#20259254 | 2 |
| #27132665 | 2 |
| C2×#131×C191 | 2 |
| #3060 | 191 |