Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C22×#14519683 | C2 | semidirect |
| 3. #21444002 | C2 | direct (N × H) |
| 4. C2×C61×#368 | C2 | semidirect |
| 15. C2×#14519683 | C22 | semidirect |
| 19. C61×#368 | C22 | semidirect |
| 109. C2×#368 | D61 | semidirect |
| 113. C2×C61 | #1417 | semidirect |
| 130. #368 | C2×D61 | semidirect |
| 131. C61 | C2×#1417 | semidirect |
| 221. C2 | #21444002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840194 | 2 |
| C22×#14519683 | 2 |
| #21444002 | 2 |
| C2×C61×#368 | 2 |
| C2×#1417 | 61 |