Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21447607 | C2 | semidirect |
| 5. #21446562 | C2 | semidirect |
| 6. #21443925 | C2 | semidirect |
| 7. C61×#1377 | C2 | semidirect |
| 21. #16839573 | C4 | semidirect |
| 54. #14519709 | C2×C4 | semidirect |
| 66. M32×C61 | C2×C4 | semidirect |
| 113. Dic244 | C4⋊C4 | semidirect |
| 115. D488 | C4⋊C4 | semidirect |
| 182. #1377 | D61 | semidirect |
| 209. C61 | #12943 | semidirect |
| 236. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454621 | 2 |
| #21447607 | 2 |
| C2×#16839573 | 2 |
| #21447532 | 2 |
| #21446562 | 2 |
| #21443925 | 2 |
| C61×#1377 | 2 |
| #12943 | 61 |