Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16840498 | C2 | semidirect |
| 2. C2×#16839959 | C2 | semidirect |
| 3. #21444876 | C2 | direct (N × H) |
| 4. C2×#16839506 | C2 | semidirect |
| 5. C2×#16839494 | C2 | semidirect |
| 10. #16840498 | C22 | semidirect |
| 16. #16839959 | C22 | semidirect |
| 19. #16839506 | C22 | semidirect |
| 20. #16839494 | C22 | semidirect |
| 168. C2×C61 | #1620 | semidirect |
| 191. C61 | C2×#1620 | semidirect |
| 326. C2 | #21444876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840498 | 2 |
| C2×#16839959 | 2 |
| #21444876 | 2 |
| C2×#16839506 | 2 |
| C2×#16839494 | 2 |
| C2×C61×#493 | 2 |
| C2×#1620 | 61 |