Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1214 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 320 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 |
|---|---|---|
| 3. C2×#16840675 | C2 | direct (N × H) |
| 11. #16840675 | C22 | direct (N × H) |
| 13. C22×Dic244 | C4 | semidirect |
| 17. C2×Q16×D61 | C4 | semidirect |
| 20. C22×Q16×C61 | C4 | semidirect |
| 38. C2×Dic244 | C2×C4 | semidirect |
| 44. Q16×D61 | C2×C4 | semidirect |
| 53. C2×Q16×C61 | C2×C4 | semidirect |
| 82. Q16×C61 | C22×C4 | semidirect |
| 90. Dic244 | C22×C4 | semidirect |
| 128. C22×C61 | #358 | semidirect |
| 130. C2×D61 | #358 | semidirect |
| 146. C2×C61 | C2×#358 | semidirect |
| 148. D61 | C2×#358 | semidirect |
| 158. C22×Q16 | #6923 | semidirect |
| 167. C61 | C22×#358 | semidirect |
| 188. C2×Q16 | C2×#6923 | semidirect |
| 231. Q16 | C22×#6923 | semidirect |
| 279. C22 | #16840675 | direct (N × H) |
| 291. C2 | C2×#16840675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D61⋊C16 | 2 |
| C22×#14519846 | 2 |
| C2×#16840675 | 2 |
| C22×Q16×D61 | 2 |
| C22×#358 | 61 |