Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1450 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 299 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×#16840153 | C2 | semidirect |
| 2. C2×#16840142 | C2 | semidirect |
| 3. C2×#16840141 | C2 | semidirect |
| 5. #21454215 | C2 | semidirect |
| 7. C4×#14519687 | C2 | semidirect |
| 51. #14519687 | D4 | semidirect |
| 140. C4×C61 | #497 | semidirect |
| 179. C61 | #33305 | semidirect |
| 292. C4 | #16840153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840153 | 2 |
| C2×#16840142 | 2 |
| C2×#16840141 | 2 |
| C2×#16840134 | 2 |
| #21454215 | 2 |
| #21454175 | 2 |
| C4×#14519687 | 2 |
| C2×C61×#492 | 2 |
| #33305 | 61 |