Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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×D4304 | C2 | semidirect |
| 2. #31770982 | C2 | semidirect |
| 3. C4×D2152 | C2 | semidirect |
| 4. #31770407 | C2 | semidirect |
| 5. C4⋊C16×C269 | C2 | semidirect |
| 25. D2152 | D4 | semidirect |
| 56. C4×C269 | D16 | semidirect |
| 65. C269 | #2206 | semidirect |
| 70. C4⋊C16 | D269 | semidirect |
| 123. C4 | D4304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4304 | 2 |
| #31770982 | 2 |
| C4×D2152 | 2 |
| #31770407 | 2 |
| C4⋊C16×C269 | 2 |
| #2206 | 269 |