Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771312 | C2 | semidirect |
| 2. #31771276 | C2 | semidirect |
| 3. #31770968 | C2 | semidirect |
| 4. #31770952 | C2 | semidirect |
| 5. #31770908 | C2 | semidirect |
| 6. #31770895 | C2 | semidirect |
| 7. #31770800 | C2 | semidirect |
| 8. #31770798 | C2 | semidirect |
| 9. #31770735 | C2 | semidirect |
| 10. #31770714 | C2 | semidirect |
| 11. C4×D8×C269 | C2 | semidirect |
| 94. D4×C269 | #41 | semidirect |
| 129. C269 | #3366 | semidirect |
| 141. C4×D8 | D269 | semidirect |
| 218. D4 | #16864402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771312 | 2 |
| #31771276 | 2 |
| #31770968 | 2 |
| #31770952 | 2 |
| #31770908 | 2 |
| #31770895 | 2 |
| #31770800 | 2 |
| #31770798 | 2 |
| #31770735 | 2 |
| #31770714 | 2 |
| C4×D8×C269 | 2 |
| #3366 | 269 |