Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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. C2×#20259341 | C2 | semidirect |
| 2. #27133211 | C2 | semidirect |
| 3. C4×#15690286 | C2 | semidirect |
| 4. #27132884 | C2 | semidirect |
| 5. #27132876 | C2 | semidirect |
| 6. #27132874 | C2 | semidirect |
| 7. #27132868 | C2 | semidirect |
| 8. #27132860 | C2 | semidirect |
| 9. C4⋊C8×D191 | C2 | semidirect |
| 10. #27132656 | C2 | semidirect |
| 11. #459×C191 | C2 | semidirect |
| 47. #15690286 | D4 | semidirect |
| 135. C4×C191 | #135 | semidirect |
| 150. C191 | #3035 | semidirect |
| 160. #459 | D191 | semidirect |
| 292. C4 | #20259341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259341 | 2 |
| #27133211 | 2 |
| C4×#15690286 | 2 |
| #27132884 | 2 |
| #27132876 | 2 |
| #27132874 | 2 |
| #27132868 | 2 |
| #27132860 | 2 |
| C4⋊C8×D191 | 2 |
| #27132656 | 2 |
| #459×C191 | 2 |
| #3035 | 191 |