Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic269 | C2 | semidirect |
| 3. #31770941 | C2 | semidirect |
| 5. #31770914 | C2 | semidirect |
| 6. #31770825 | C2 | semidirect |
| 7. #31770761 | C2 | semidirect |
| 8. #31770709 | C2 | semidirect |
| 9. #31770706 | C2 | semidirect |
| 10. #31770659 | C2 | semidirect |
| 131. C269 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771136 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770941 | 2 |
| #31770921 | 2 |
| #31770914 | 2 |
| #31770825 | 2 |
| #31770761 | 2 |
| #31770709 | 2 |
| #31770706 | 2 |
| #31770659 | 2 |
| #448×C269 | 2 |
| #3117 | 269 |