Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21460791 | C2 | direct (N × H) |
| 15. #16840017 | C4 | semidirect |
| 17. C2×#14519709 | C4 | semidirect |
| 19. C22×Q16×C61 | C4 | semidirect |
| 46. #14519709 | C2×C4 | semidirect |
| 53. C2×Q16×C61 | C2×C4 | semidirect |
| 167. C2×C61 | #1340 | semidirect |
| 171. C22×Q16 | #6923 | semidirect |
| 186. C61 | C2×#1340 | semidirect |
| 192. C2×Q16 | C2×#6923 | semidirect |
| 331. C2 | #21460791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840659 | 2 |
| C2×#16840630 | 2 |
| #21460791 | 2 |
| C2×#16840017 | 2 |
| C2×#1340 | 61 |