Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575485 | C2 | semidirect |
| 2. C2×#22575482 | C2 | semidirect |
| 4. C4⋊Q8×D269 | C2 | semidirect |
| 5. #31771000 | C2 | semidirect |
| 6. #31770999 | C2 | semidirect |
| 7. #31770997 | C2 | semidirect |
| 8. #31770983 | C2 | semidirect |
| 9. #31770976 | C2 | semidirect |
| 10. #31770557 | C2 | semidirect |
| 11. #497×C269 | C2 | semidirect |
| 63. #16864385 | D4 | semidirect |
| 124. Dic269 | #137 | semidirect |
| 130. C269 | #3152 | semidirect |
| 139. #497 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575485 | 2 |
| C2×#22575482 | 2 |
| #31771154 | 2 |
| C4⋊Q8×D269 | 2 |
| #31771000 | 2 |
| #31770999 | 2 |
| #31770997 | 2 |
| #31770983 | 2 |
| #31770976 | 2 |
| #31770557 | 2 |
| #497×C269 | 2 |
| #3152 | 269 |