Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#16839875 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. C2×#16839572 | C2 | semidirect |
| 5. #21443919 | C2 | semidirect |
| 6. #21443899 | C2 | semidirect |
| 7. C61×#1975 | C2 | semidirect |
| 12. C2×#14519720 | C4 | semidirect |
| 13. C2×#14519718 | C4 | semidirect |
| 46. C2×#11758185 | C2×C4 | semidirect |
| 55. C2×Q16×C61 | C2×C4 | semidirect |
| 57. C2×D8×C61 | C2×C4 | semidirect |
| 177. #1975 | D61 | semidirect |
| 205. C61 | #13037 | semidirect |
| 213. C2×Q16 | C4×D61 | semidirect |
| 221. C2×D8 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C2×#16839875 | 2 |
| C2×#16839574 | 2 |
| C2×#16839572 | 2 |
| #21443919 | 2 |
| #21443899 | 2 |
| C61×#1975 | 2 |
| #13037 | 61 |