Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771320 | C2 | semidirect |
| 2. #31771259 | C2 | semidirect |
| 3. #31771003 | C2 | semidirect |
| 4. #31770930 | C2 | semidirect |
| 5. #31770924 | C2 | semidirect |
| 6. #31770896 | C2 | semidirect |
| 7. #31770886 | C2 | semidirect |
| 8. #31770858 | C2 | semidirect |
| 9. C4×D2152 | C2 | semidirect |
| 10. #31770647 | C2 | semidirect |
| 11. #436×C269 | C2 | semidirect |
| 101. C8×C269 | #41 | semidirect |
| 127. C269 | #3354 | semidirect |
| 138. #436 | D269 | semidirect |
| 229. C8 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31771259 | 2 |
| #31771003 | 2 |
| #31770930 | 2 |
| #31770924 | 2 |
| #31770896 | 2 |
| #31770886 | 2 |
| #31770858 | 2 |
| C4×D2152 | 2 |
| #31770647 | 2 |
| #436×C269 | 2 |
| #3354 | 269 |