Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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×#16839599 | C2 | semidirect |
| 2. #21448113 | C2 | semidirect |
| 4. #21444022 | C2 | semidirect |
| 5. #21444012 | C2 | semidirect |
| 6. #21444008 | C2 | semidirect |
| 7. C61×#2222 | C2 | semidirect |
| 90. #2222 | D61 | semidirect |
| 114. C61 | #13702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839599 | 2 |
| #21448113 | 2 |
| #21447939 | 2 |
| #21444022 | 2 |
| #21444012 | 2 |
| #21444008 | 2 |
| C61×#2222 | 2 |
| #13702 | 61 |