Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#14519721 | C2 | semidirect |
| 2. C2×#16840037 | C2 | semidirect |
| 3. C2×#16839575 | C2 | semidirect |
| 4. #21447538 | C2 | semidirect |
| 5. C2×#16839546 | C2 | semidirect |
| 6. #21443914 | C2 | semidirect |
| 37. C2×Dic244 | D4 | semidirect |
| 47. C2×#11758185 | D4 | semidirect |
| 49. #14519713 | D4 | semidirect |
| 223. C61 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519721 | 2 |
| C2×#16840037 | 2 |
| C2×#16839575 | 2 |
| #21447538 | 2 |
| C2×#16839546 | 2 |
| #21443914 | 2 |
| C61×#3058 | 2 |
| #13321 | 61 |