Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #31770658 | C2 | semidirect |
| 3. #31770335 | C2 | semidirect |
| 4. #31770332 | C2 | semidirect |
| 5. C2×C4⋊C8×C269 | C2 | semidirect |
| 24. #16864402 | C8 | semidirect |
| 53. Dic538 | C2×C8 | semidirect |
| 55. D1076 | C2×C8 | semidirect |
| 101. C269 | #1477 | semidirect |
| 105. C2×C4⋊C8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864402 | 2 |
| #31770658 | 2 |
| #31770335 | 2 |
| #31770332 | 2 |
| C2×C4⋊C8×C269 | 2 |
| #1477 | 269 |