Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
624 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21454890 | C2 | semidirect |
| 2. #21447484 | C2 | semidirect |
| 3. #21445783 | C2 | semidirect |
| 4. #21443949 | C2 | semidirect |
| 19. C61×#456 | C4 | semidirect |
| 21. C61×#454 | C4 | semidirect |
| 203. #456 | Dic61 | semidirect |
| 205. #454 | Dic61 | semidirect |
| 219. C61 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454890 | 2 |
| #21447484 | 2 |
| #21445783 | 2 |
| #21443949 | 2 |
| C61×#3018 | 2 |
| #13053 | 61 |