Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #21447428 | C2 | semidirect |
| 3. C22⋊C16×D61 | C2 | semidirect |
| 4. #21443758 | C2 | semidirect |
| 5. #21443758 | C2 | semidirect |
| 6. #21443743 | C2 | semidirect |
| 7. C61×#1314 | C2 | semidirect |
| 188. #1314 | D61 | semidirect |
| 216. C61 | #11467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839836 | 2 |
| #21447428 | 2 |
| C22⋊C16×D61 | 2 |
| #21443758 | 2 |
| #21443743 | 2 |
| C61×#1314 | 2 |
| #11467 | 61 |