Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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×#11762648 | C2 | semidirect |
| 3. C4×Dic136 | C2 | semidirect |
| 4. #14526963 | C2 | semidirect |
| 5. C17×C4⋊C32 | C2 | semidirect |
| 27. Dic136 | D4 | semidirect |
| 69. C4⋊C32 | D17 | semidirect |
| 76. C4×C17 | SD64 | semidirect |
| 111. C17 | #13686 | semidirect |
| 152. C4 | #11762648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762648 | 2 |
| #14531034 | 2 |
| C4×Dic136 | 2 |
| #14526963 | 2 |
| C17×C4⋊C32 | 2 |
| #13686 | 17 |