Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1806 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 667 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. #14537053 | C2 | direct (N × H) |
| 33. C2×C42×C17 | Q8 | semidirect |
| 62. C42×C17 | C2×Q8 | semidirect |
| 117. C2×C17 | #2843 | semidirect |
| 136. C2×C42 | Dic34 | semidirect |
| 142. C17 | C2×#2843 | semidirect |
| 164. C42 | C2×Dic34 | semidirect |
| 195. C2 | #14537053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537053 | 2 |
| C2×#11762748 | 2 |
| C2×#11762742 | 2 |
| C2×#11762729 | 2 |
| C2×#11762677 | 2 |
| C2×C17×#384 | 2 |
| C2×#2843 | 17 |