Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
914 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 914 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×#16840167 | C2 | semidirect |
| 2. C2×#16840142 | C2 | semidirect |
| 5. #21445490 | C2 | direct (N × H) |
| 6. C2×C61×#322 | C2 | semidirect |
| 13. #16840167 | C22 | semidirect |
| 15. #16840142 | C22 | semidirect |
| 24. C61×#322 | C22 | semidirect |
| 129. C2×#322 | D61 | semidirect |
| 130. C2×C61 | #1722 | semidirect |
| 151. #322 | C2×D61 | semidirect |
| 152. C61 | C2×#1722 | semidirect |
| 252. C2 | #21445490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840167 | 2 |
| C2×#16840142 | 2 |
| C2×#16840135 | 2 |
| C2×#16840109 | 2 |
| #21445490 | 2 |
| C2×C61×#322 | 2 |
| C2×#1722 | 61 |