Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31770641 | C2 | semidirect |
| 3. #31770623 | C2 | semidirect |
| 4. #31770622 | C2 | semidirect |
| 5. #31770578 | C2 | semidirect |
| 6. #31770561 | C2 | semidirect |
| 7. #410×C269 | C2 | semidirect |
| 13. C2×#16864392 | C4 | semidirect |
| 14. C2×#16864390 | C4 | semidirect |
| 15. C2×#16864389 | C4 | semidirect |
| 16. C2×#16864387 | C4 | semidirect |
| 132. C269 | #1976 | semidirect |
| 139. #410 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575473 | 2 |
| #31770641 | 2 |
| #31770623 | 2 |
| #31770622 | 2 |
| #31770578 | 2 |
| #31770561 | 2 |
| #410×C269 | 2 |
| #1976 | 269 |