Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21448542 | C2 | semidirect |
| 3. #21446652 | C2 | semidirect |
| 4. #21444486 | C2 | semidirect |
| 5. #21443677 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 7. C61×#1517 | C2 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 51. C4×#92418 | C2×C4 | semidirect |
| 55. C4⋊Q8×C61 | C2×C4 | semidirect |
| 56. #127×C61 | C2×C4 | semidirect |
| 119. C4×Dic61 | D8 | semidirect |
| 209. #1517 | D61 | semidirect |
| 238. C61 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D61 | semidirect |
| 251. #127 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21448542 | 2 |
| #21446652 | 2 |
| #21444486 | 2 |
| #21443677 | 2 |
| #21443647 | 2 |
| C61×#1517 | 2 |
| #9299 | 61 |