Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#20259342 | C2 | semidirect |
| 2. #27133213 | C2 | semidirect |
| 3. #27133058 | C2 | semidirect |
| 4. #27133055 | C2 | semidirect |
| 5. #27133053 | C2 | semidirect |
| 6. #27133050 | C2 | semidirect |
| 7. C2×#20259233 | C2 | semidirect |
| 8. #532×C191 | C2 | semidirect |
| 40. C2×C191⋊C8 | D4 | semidirect |
| 97. C191 | #3150 | semidirect |
| 101. #532 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259342 | 2 |
| #27133213 | 2 |
| #27133058 | 2 |
| #27133055 | 2 |
| #27133053 | 2 |
| #27133050 | 2 |
| C2×#20259233 | 2 |
| #532×C191 | 2 |
| #3150 | 191 |