Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447569 | C2 | semidirect |
| 3. #21447568 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. #21446573 | C2 | semidirect |
| 6. #21443898 | C2 | semidirect |
| 7. C61×#2145 | C2 | semidirect |
| 74. #106×C61 | D4 | semidirect |
| 190. #2145 | D61 | semidirect |
| 220. C61 | #13416 | semidirect |
| 263. #106 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456262 | 2 |
| #21447569 | 2 |
| #21447568 | 2 |
| #21447554 | 2 |
| #21446573 | 2 |
| #21443898 | 2 |
| C61×#2145 | 2 |
| #13416 | 61 |