Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #21447605 | C2 | semidirect |
| 5. #21443927 | C2 | semidirect |
| 6. #21443915 | C2 | semidirect |
| 7. C2×C61×#366 | C2 | semidirect |
| 20. #16839545 | C4 | semidirect |
| 42. #14519717 | C2×C4 | semidirect |
| 58. C2×C16×C61 | C2×C4 | semidirect |
| 154. C2×#366 | D61 | semidirect |
| 183. C61 | #12925 | semidirect |
| 207. C2×C16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454415 | 2 |
| #21447605 | 2 |
| C2×#16839545 | 2 |
| #21445884 | 2 |
| #21443927 | 2 |
| #21443915 | 2 |
| C2×C61×#366 | 2 |
| #12925 | 61 |