Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31770936 | C2 | semidirect |
| 5. #31770910 | C2 | semidirect |
| 6. #31770825 | C2 | semidirect |
| 7. #31770761 | C2 | semidirect |
| 8. #31770697 | C2 | semidirect |
| 9. SD16×Dic269 | C2 | semidirect |
| 10. #31770655 | C2 | semidirect |
| 131. C269 | #3108 | 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 |
| #31770936 | 2 |
| #31770916 | 2 |
| #31770910 | 2 |
| #31770825 | 2 |
| #31770761 | 2 |
| #31770697 | 2 |
| SD16×Dic269 | 2 |
| #31770655 | 2 |
| #448×C269 | 2 |
| #3108 | 269 |