Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21448002 | C2 | semidirect |
| 2. #21447997 | C2 | semidirect |
| 3. #21447259 | C2 | semidirect |
| 4. #21443834 | C2 | semidirect |
| 5. #21443834 | C2 | semidirect |
| 6. #21443745 | C2 | semidirect |
| 8. C2×#14519711 | C22 | semidirect |
| 14. C22⋊#11758185 | C22 | semidirect |
| 15. C22⋊#11758185 | C22 | semidirect |
| 17. #16839527 | C22 | semidirect |
| 190. C61 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448002 | 2 |
| #21447997 | 2 |
| #21447259 | 2 |
| #21443834 | 2 |
| #21443745 | 2 |
| C61×#3199 | 2 |
| #12284 | 61 |