Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #27133237 | C2 | semidirect |
| 3. #27133146 | C2 | semidirect |
| 4. #27132887 | C2 | semidirect |
| 5. #27132880 | C2 | semidirect |
| 6. #27132871 | C2 | semidirect |
| 7. #27132866 | C2 | semidirect |
| 8. #27132691 | C2 | semidirect |
| 9. #27132665 | C2 | semidirect |
| 10. C2×#20259246 | C2 | semidirect |
| 11. C2×#137×C191 | C2 | semidirect |
| 146. C191 | #3046 | semidirect |
| 148. C2×#137 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259342 | 2 |
| #27133237 | 2 |
| #27133146 | 2 |
| #27132887 | 2 |
| #27132880 | 2 |
| #27132871 | 2 |
| #27132866 | 2 |
| #27132691 | 2 |
| #27132665 | 2 |
| C2×#20259246 | 2 |
| C2×#137×C191 | 2 |
| #3046 | 191 |