Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1422 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 224 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×#16840741 | C2 | semidirect |
| 2. #21462098 | C2 | direct (N × H) |
| 3. C2×#16840666 | C2 | semidirect |
| 7. #16840741 | C22 | semidirect |
| 8. C2×#14519836 | C22 | semidirect |
| 10. #16840666 | C22 | semidirect |
| 13. #16840329 | C4 | semidirect |
| 16. C2×#14519764 | C4 | semidirect |
| 19. C2×#14519736 | C4 | semidirect |
| 20. C23×D4×C61 | C4 | semidirect |
| 27. #14519836 | C23 | semidirect |
| 43. #14519764 | C2×C4 | semidirect |
| 49. #14519736 | C2×C4 | semidirect |
| 60. C22×D4×C61 | C2×C4 | semidirect |
| 205. C2×C61 | #2128 | semidirect |
| 210. C23×D4 | #6923 | semidirect |
| 225. C61 | C2×#2128 | semidirect |
| 241. C22×D4 | C2×#6923 | semidirect |
| 407. C2 | #21462098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840741 | 2 |
| #21462098 | 2 |
| C2×#16840666 | 2 |
| C2×#16840329 | 2 |
| C2×#2128 | 61 |