Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #31770888 | C2 | semidirect |
| 6. #31770813 | C2 | semidirect |
| 8. #31770712 | C2 | semidirect |
| 9. #31770709 | C2 | semidirect |
| 127. C269 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771157 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770936 | 2 |
| #31770933 | 2 |
| #31770888 | 2 |
| #31770813 | 2 |
| #31770761 | 2 |
| #31770712 | 2 |
| #31770709 | 2 |
| #31770659 | 2 |
| #451×C269 | 2 |
| #3113 | 269 |