Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #31771320 | C2 | semidirect |
| 2. #31771260 | C2 | semidirect |
| 3. #31771003 | C2 | semidirect |
| 4. #31770928 | C2 | semidirect |
| 5. #31770922 | C2 | semidirect |
| 6. #31770895 | C2 | semidirect |
| 7. #31770885 | C2 | semidirect |
| 8. #31770855 | C2 | semidirect |
| 9. #31770684 | C2 | semidirect |
| 10. #31770646 | C2 | semidirect |
| 11. C4×D8×C269 | C2 | semidirect |
| 101. C8×C269 | #41 | semidirect |
| 127. C269 | #3354 | semidirect |
| 137. C4×D8 | D269 | semidirect |
| 229. C8 | #16864402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31771260 | 2 |
| #31771003 | 2 |
| #31770928 | 2 |
| #31770922 | 2 |
| #31770895 | 2 |
| #31770885 | 2 |
| #31770855 | 2 |
| #31770684 | 2 |
| #31770646 | 2 |
| C4×D8×C269 | 2 |
| #3354 | 269 |