Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16864391 | C2 | semidirect |
| 2. C2×#22575459 | C2 | semidirect |
| 3. #31771181 | C2 | semidirect |
| 5. #31770852 | C2 | semidirect |
| 6. #31770835 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 8. #31770609 | C2 | semidirect |
| 9. #427×C269 | C2 | semidirect |
| 18. C2×#16864385 | C22 | semidirect |
| 19. C2×C8×D269 | C22 | semidirect |
| 25. #22575433 | C22 | semidirect |
| 28. #22575376 | C22 | semidirect |
| 33. #107×C269 | C22 | semidirect |
| 34. #106×C269 | C22 | semidirect |
| 62. C2×C8×C269 | D4 | semidirect |
| 120. C269 | #3057 | semidirect |
| 128. #427 | D269 | semidirect |
| 152. #107 | C2×D269 | semidirect |
| 153. #106 | C2×D269 | semidirect |
| 180. C2×C8 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864391 | 2 |
| C2×#22575459 | 2 |
| #31771181 | 2 |
| #31771174 | 2 |
| #31770852 | 2 |
| #31770835 | 2 |
| #31770613 | 2 |
| #31770609 | 2 |
| #427×C269 | 2 |
| #3057 | 269 |