Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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×#16840160 | C2 | semidirect |
| 3. C2×#16840113 | C2 | semidirect |
| 5. #21445420 | C2 | direct (N × H) |
| 6. C2×C82×C61 | C2 | semidirect |
| 12. #16840160 | C22 | semidirect |
| 16. #16840113 | C22 | semidirect |
| 24. C82×C61 | C22 | semidirect |
| 127. C2×C82 | D61 | semidirect |
| 128. C2×C61 | #1708 | semidirect |
| 149. C82 | C2×D61 | semidirect |
| 150. C61 | C2×#1708 | semidirect |
| 248. C2 | #21445420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840160 | 2 |
| C2×#16840135 | 2 |
| C2×#16840113 | 2 |
| C2×#16840109 | 2 |
| #21445420 | 2 |
| C2×C82×C61 | 2 |
| C2×#1708 | 61 |