Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #21447539 | C2 | semidirect |
| 5. #21443925 | C2 | semidirect |
| 6. #21443924 | C2 | semidirect |
| 7. C61×#2141 | C2 | semidirect |
| 13. #16840017 | C4 | semidirect |
| 53. #14519709 | C2×C4 | semidirect |
| 62. C2×Q16×C61 | C2×C4 | semidirect |
| 176. #2141 | D61 | semidirect |
| 203. C61 | #13000 | semidirect |
| 211. C2×Q16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840017 | 2 |
| #21454407 | 2 |
| #21447539 | 2 |
| C2×#16839543 | 2 |
| #21443925 | 2 |
| #21443924 | 2 |
| C61×#2141 | 2 |
| #13000 | 61 |