Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771316 | C2 | semidirect |
| 2. #31771276 | C2 | semidirect |
| 3. #31770968 | C2 | semidirect |
| 4. #31770953 | C2 | semidirect |
| 5. #31770904 | C2 | semidirect |
| 6. #31770801 | C2 | semidirect |
| 7. #31770799 | C2 | semidirect |
| 8. #31770732 | C2 | semidirect |
| 9. #31770716 | C2 | semidirect |
| 10. C4×#16864387 | C2 | semidirect |
| 11. #476×C269 | C2 | semidirect |
| 82. D1076 | #41 | semidirect |
| 129. C269 | #3366 | semidirect |
| 136. #476 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771316 | 2 |
| #31771276 | 2 |
| #31770968 | 2 |
| #31770953 | 2 |
| #31770904 | 2 |
| #31770801 | 2 |
| #31770799 | 2 |
| #31770732 | 2 |
| #31770716 | 2 |
| C4×#16864387 | 2 |
| #476×C269 | 2 |
| #3366 | 269 |