Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16840180 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. #21445870 | C2 | semidirect |
| 5. #21443931 | C2 | semidirect |
| 6. #21443914 | C2 | semidirect |
| 7. C61×#2145 | C2 | semidirect |
| 15. #16840034 | C4 | semidirect |
| 16. #16840029 | C4 | semidirect |
| 177. #2145 | D61 | semidirect |
| 209. C61 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840180 | 2 |
| #21455535 | 2 |
| C2×#16839569 | 2 |
| #21445870 | 2 |
| #21443931 | 2 |
| #21443914 | 2 |
| C61×#2145 | 2 |
| #13071 | 61 |