Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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×#11762646 | C2 | semidirect |
| 3. C4⋊#10587465 | C2 | semidirect |
| 4. #14526961 | C2 | semidirect |
| 5. C4×C17×Q32 | C2 | semidirect |
| 22. C17×Q32 | D4 | semidirect |
| 68. C4×Q32 | D17 | semidirect |
| 78. C4×C17 | SD64 | semidirect |
| 101. Q32 | D68 | semidirect |
| 111. C17 | #13686 | semidirect |
| 152. C4 | #11762646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762646 | 2 |
| #14531034 | 2 |
| C4⋊#10587465 | 2 |
| #14526961 | 2 |
| C4×C17×Q32 | 2 |
| #13686 | 17 |