Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 4. #14531035 | C2 | direct (N × H) |
| 93. C2×Dic17 | Q32 | semidirect |
| 116. Dic17 | C2×Q32 | semidirect |
| 133. C2×C17 | #2247 | semidirect |
| 163. C17 | C2×#2247 | semidirect |
| 224. C2 | #14531035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic136 | 2 |
| C22×#10587500 | 2 |
| C2×#11763187 | 2 |
| #14531035 | 2 |
| C2×C16×Dic17 | 2 |
| C22×C17×Q32 | 2 |
| C2×#2247 | 17 |