Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16840159 | C2 | semidirect |
| 5. #21443919 | C2 | semidirect |
| 6. #21443900 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 29. C2×Dic244 | Q8 | semidirect |
| 31. C2×D488 | Q8 | semidirect |
| 149. #1383 | D61 | semidirect |
| 171. C61 | #13371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840159 | 2 |
| C2×#16839573 | 2 |
| C2×#16839571 | 2 |
| #21446705 | 2 |
| #21443919 | 2 |
| #21443900 | 2 |
| C61×#1383 | 2 |
| #13371 | 61 |