Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
696 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×#14519832 | C2 | semidirect |
| 2. #21461545 | C2 | semidirect |
| 3. C2×#16840617 | C2 | semidirect |
| 4. #21460695 | C2 | semidirect |
| 35. #14519832 | D4 | semidirect |
| 184. C22×C61 | #329 | semidirect |
| 235. C61 | #9119 | semidirect |
| 394. C22 | #16840617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519832 | 2 |
| #21461545 | 2 |
| C2×#16840617 | 2 |
| #21460695 | 2 |
| #21454118 | 2 |
| #9119 | 61 |