Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. C2×#22575474 | C2 | semidirect |
| 2. #31771259 | C2 | semidirect |
| 3. #31771258 | C2 | semidirect |
| 4. #31770984 | C2 | semidirect |
| 5. #31770845 | C2 | semidirect |
| 6. #31770811 | C2 | semidirect |
| 7. #31770770 | C2 | semidirect |
| 8. #31770764 | C2 | semidirect |
| 9. C4×#16864387 | C2 | semidirect |
| 10. #31770670 | C2 | semidirect |
| 11. #461×C269 | C2 | semidirect |
| 58. #16864387 | D4 | semidirect |
| 126. C4×C269 | #135 | semidirect |
| 138. C269 | #3283 | semidirect |
| 146. #461 | D269 | semidirect |
| 268. C4 | #22575474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575474 | 2 |
| #31771259 | 2 |
| #31771258 | 2 |
| #31770984 | 2 |
| #31770845 | 2 |
| #31770811 | 2 |
| #31770770 | 2 |
| #31770764 | 2 |
| C4×#16864387 | 2 |
| #31770670 | 2 |
| #461×C269 | 2 |
| #3283 | 269 |