Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C4×#14519692 | C2 | semidirect |
| 2. #21444137 | C2 | semidirect |
| 3. #21443840 | C2 | semidirect |
| 4. #21443816 | C2 | semidirect |
| 12. C2×#124×C61 | C4 | semidirect |
| 15. C61×#393 | C4 | semidirect |
| 18. C61×#392 | C4 | semidirect |
| 22. C61×#383 | C4 | semidirect |
| 203. C2×#124 | Dic61 | semidirect |
| 208. #393 | Dic61 | semidirect |
| 211. #392 | Dic61 | semidirect |
| 215. #383 | Dic61 | semidirect |
| 220. C61 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519692 | 2 |
| #21444137 | 2 |
| #21443840 | 2 |
| #21443816 | 2 |
| C61×#2631 | 2 |
| #11730 | 61 |