Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16840200 | C2 | semidirect |
| 2. #21455428 | C2 | semidirect |
| 3. C2×#16840015 | C2 | semidirect |
| 4. C2×#16839573 | C2 | semidirect |
| 5. #21447536 | C2 | semidirect |
| 6. #21443925 | C2 | semidirect |
| 7. C2×C61×#349 | C2 | semidirect |
| 38. C2×Dic244 | D4 | semidirect |
| 45. C2×D488 | D4 | semidirect |
| 46. C2×D488 | D4 | semidirect |
| 59. #14519711 | D4 | semidirect |
| 62. #14519709 | D4 | semidirect |
| 78. M32×C61 | D4 | semidirect |
| 219. C2×#349 | D61 | semidirect |
| 251. C61 | #13316 | semidirect |
| 292. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| #21455428 | 2 |
| C2×#16840015 | 2 |
| C2×#16839573 | 2 |
| #21447536 | 2 |
| #21443925 | 2 |
| C2×C61×#349 | 2 |
| #13316 | 61 |