Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #31771328 | C2 | semidirect |
| 2. Q8×D1076 | C2 | semidirect |
| 3. #31770965 | C2 | semidirect |
| 4. #31770956 | C2 | semidirect |
| 5. #31770901 | C2 | semidirect |
| 6. #31770886 | C2 | semidirect |
| 8. #31770811 | C2 | semidirect |
| 9. #31770707 | C2 | semidirect |
| 11. #446×C269 | C2 | semidirect |
| 122. C269 | #3367 | semidirect |
| 132. #446 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| Q8×D1076 | 2 |
| #31770965 | 2 |
| #31770956 | 2 |
| #31770901 | 2 |
| #31770886 | 2 |
| #31770821 | 2 |
| #31770811 | 2 |
| #31770707 | 2 |
| C4×D2152 | 2 |
| #446×C269 | 2 |
| #3367 | 269 |