Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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. #27132972 | C2 | semidirect |
| 5. #27132959 | C2 | semidirect |
| 6. #27132958 | C2 | semidirect |
| 7. #27132945 | C2 | semidirect |
| 11. #475×C191 | C2 | semidirect |
| 47. Q8×D191 | Q8 | semidirect |
| 130. C191 | #3078 | semidirect |
| 139. #475 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| C4×Q8×D191 | 2 |
| #27132973 | 2 |
| #27132972 | 2 |
| #27132959 | 2 |
| #27132958 | 2 |
| #27132945 | 2 |
| #27132702 | 2 |
| #27132685 | 2 |
| #27132670 | 2 |
| #475×C191 | 2 |
| #3078 | 191 |