Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
534 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 156 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×C4⋊#11758187 | C2 | semidirect |
| 2. C2×#16840657 | C2 | semidirect |
| 3. C2×C4×#11758187 | C2 | semidirect |
| 21. C2×#11758187 | D4 | semidirect |
| 47. C2×D244 | C16 | semidirect |
| 107. C4×C61 | C22⋊C16 | semidirect |
| 134. C61 | #13189 | semidirect |
| 225. C4 | #16840657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11758187 | 2 |
| C2×#16840657 | 2 |
| C2×C4×#11758187 | 2 |
| C2×#16839827 | 2 |
| #13189 | 61 |