Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 1. #27133218 | C2 | semidirect |
| 3. #27132968 | C2 | semidirect |
| 4. #27132962 | C2 | semidirect |
| 5. #27132958 | C2 | semidirect |
| 6. #27132954 | C2 | semidirect |
| 7. #27132940 | C2 | semidirect |
| 8. #27132698 | C2 | semidirect |
| 9. C4⋊C8×D191 | C2 | semidirect |
| 11. #475×C191 | C2 | semidirect |
| 44. #15690288 | Q8 | semidirect |
| 134. C191 | #3076 | semidirect |
| 142. #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×#15690288 | 2 |
| #27132968 | 2 |
| #27132962 | 2 |
| #27132958 | 2 |
| #27132954 | 2 |
| #27132940 | 2 |
| #27132698 | 2 |
| C4⋊C8×D191 | 2 |
| #27132658 | 2 |
| #475×C191 | 2 |
| #3076 | 191 |