Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
662 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 280 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. C2×#16840690 | C2 | direct (N × H) |
| 7. #16840690 | C22 | direct (N × H) |
| 69. C22×C61 | #368 | semidirect |
| 82. C2×C61 | C2×#368 | semidirect |
| 95. C61 | C22×#368 | semidirect |
| 155. C22 | #16840690 | direct (N × H) |
| 163. C2 | C2×#16840690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519848 | 2 |
| C2×#16840690 | 2 |
| C22×C16×D61 | 2 |
| C22×#368 | 61 |