Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16840197 | C2 | semidirect |
| 2. C2×#16840032 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. C2×#16839562 | C2 | semidirect |
| 5. C2×#16839546 | C2 | semidirect |
| 6. #21443927 | C2 | semidirect |
| 7. C61×#3061 | C2 | semidirect |
| 40. C2×D488 | D4 | semidirect |
| 46. #14519717 | D4 | semidirect |
| 52. #14519713 | D4 | semidirect |
| 213. #3061 | D61 | semidirect |
| 249. C61 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C2×#16840032 | 2 |
| C2×#16839569 | 2 |
| C2×#16839562 | 2 |
| C2×#16839546 | 2 |
| #21443927 | 2 |
| C61×#3061 | 2 |
| #13307 | 61 |