Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22575482 | C2 | semidirect |
| 3. C4×Q8×D269 | C2 | semidirect |
| 4. #31770826 | C2 | semidirect |
| 5. #31770825 | C2 | semidirect |
| 6. #31770816 | C2 | semidirect |
| 7. #31770815 | C2 | semidirect |
| 8. #31770802 | C2 | semidirect |
| 9. #31770627 | C2 | semidirect |
| 10. #31770603 | C2 | semidirect |
| 11. #460×C269 | C2 | semidirect |
| 50. Q8×D269 | D4 | semidirect |
| 132. C4×C269 | #137 | semidirect |
| 146. C269 | #3037 | semidirect |
| 156. #460 | D269 | semidirect |
| 285. C4 | #22575482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575482 | 2 |
| #31771153 | 2 |
| C4×Q8×D269 | 2 |
| #31770826 | 2 |
| #31770825 | 2 |
| #31770816 | 2 |
| #31770815 | 2 |
| #31770802 | 2 |
| #31770627 | 2 |
| #31770603 | 2 |
| #460×C269 | 2 |
| #3037 | 269 |