Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21447591 | C2 | semidirect |
| 2. C2×#16839578 | C2 | semidirect |
| 3. #21447539 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 184. C61 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447591 | 2 |
| C2×#16839578 | 2 |
| #21447539 | 2 |
| #21447447 | 2 |
| #21445873 | 2 |
| #21443920 | 2 |
| C61×#3059 | 2 |
| #13397 | 61 |