Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
376 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 80 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. C4⋊C8×#6923 | C2 | semidirect |
| 3. #21461389 | C2 | semidirect |
| 5. #21460711 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 23. #16839509 | C4 | semidirect |
| 24. #16839507 | C4 | semidirect |
| 25. #16839506 | C4 | semidirect |
| 26. C61×#331 | C4 | semidirect |
| 196. #331 | #6923 | semidirect |
| 199. C61 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461953 | 2 |
| C4⋊C8×#6923 | 2 |
| #21461389 | 2 |
| #21461125 | 2 |
| #21460711 | 2 |
| #21460646 | 2 |
| #21444465 | 2 |
| #9577 | 61 |