Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21448074 | C2 | semidirect |
| 2. #21447651 | C2 | semidirect |
| 3. #21445184 | C2 | semidirect |
| 4. #21443890 | C2 | semidirect |
| 5. #21443867 | C2 | semidirect |
| 6. #21443865 | C2 | semidirect |
| 73. #11758185 | D8 | semidirect |
| 140. C61 | #12435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448074 | 2 |
| #21447651 | 2 |
| #21445184 | 2 |
| #21443890 | 2 |
| #21443867 | 2 |
| #21443865 | 2 |
| C61×#1667 | 2 |
| #12435 | 61 |