Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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×#20259268 | C2 | semidirect |
| 2. C2×#20259266 | C2 | semidirect |
| 3. C2×#20259265 | C2 | semidirect |
| 5. #27133047 | C2 | semidirect |
| 6. C4×C191⋊C16 | C2 | semidirect |
| 7. #495×C191 | C2 | semidirect |
| 75. C191 | #2249 | semidirect |
| 82. #495 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259268 | 2 |
| C2×#20259266 | 2 |
| C2×#20259265 | 2 |
| C2×#20259263 | 2 |
| #27133047 | 2 |
| C4×C191⋊C16 | 2 |
| #495×C191 | 2 |
| #2249 | 191 |