Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21448044 | C2 | semidirect |
| 2. #21448043 | C2 | semidirect |
| 3. #21448042 | C2 | semidirect |
| 5. #21445428 | C2 | semidirect |
| 6. #21443735 | C2 | semidirect |
| 7. C61×#2240 | C2 | semidirect |
| 107. #2240 | D61 | semidirect |
| 131. C61 | #12513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448044 | 2 |
| #21448043 | 2 |
| #21448042 | 2 |
| #21445433 | 2 |
| #21445428 | 2 |
| #21443735 | 2 |
| C61×#2240 | 2 |
| #12513 | 61 |