Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133294 | C2 | semidirect |
| 3. #27132973 | C2 | semidirect |
| 4. #27132962 | C2 | semidirect |
| 5. #27132952 | C2 | semidirect |
| 6. #27132947 | C2 | semidirect |
| 7. #27132703 | C2 | semidirect |
| 8. #27132689 | C2 | semidirect |
| 11. C2×#106×C191 | C2 | semidirect |
| 42. #15690287 | Q8 | semidirect |
| 123. C191 | #3084 | semidirect |
| 132. C2×#106 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133294 | 2 |
| #27133144 | 2 |
| #27132973 | 2 |
| #27132962 | 2 |
| #27132952 | 2 |
| #27132947 | 2 |
| #27132703 | 2 |
| #27132689 | 2 |
| #27132662 | 2 |
| #27132660 | 2 |
| C2×#106×C191 | 2 |
| #3084 | 191 |