Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#20259354 | C2 | semidirect |
| 3. C2×Q16×D191 | C2 | semidirect |
| 4. #27133238 | C2 | semidirect |
| 5. #27133056 | C2 | semidirect |
| 6. #27133055 | C2 | semidirect |
| 7. #27133048 | C2 | semidirect |
| 8. #27133047 | C2 | semidirect |
| 9. #27133041 | C2 | semidirect |
| 10. #27132617 | C2 | semidirect |
| 11. #494×C191 | C2 | semidirect |
| 121. C191 | #3156 | semidirect |
| 132. #494 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259354 | 2 |
| C2×#20259345 | 2 |
| C2×Q16×D191 | 2 |
| #27133238 | 2 |
| #27133056 | 2 |
| #27133055 | 2 |
| #27133048 | 2 |
| #27133047 | 2 |
| #27133041 | 2 |
| #27132617 | 2 |
| #494×C191 | 2 |
| #3156 | 191 |