Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #27133001 | C2 | semidirect |
| 3. #27133001 | C2 | semidirect |
| 4. #27132996 | C2 | semidirect |
| 5. #27132991 | C2 | semidirect |
| 6. #27132706 | C2 | semidirect |
| 7. #27132699 | C2 | semidirect |
| 8. #27132672 | C2 | semidirect |
| 9. C2×#20259246 | C2 | semidirect |
| 126. C191 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133146 | 2 |
| #27133001 | 2 |
| #27132996 | 2 |
| #27132991 | 2 |
| #27132706 | 2 |
| #27132699 | 2 |
| #27132672 | 2 |
| C2×#20259246 | 2 |
| #27132630 | 2 |
| #536×C191 | 2 |
| #3097 | 191 |