Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16864390 | C2 | semidirect |
| 2. C2×#22575461 | C2 | semidirect |
| 3. #31771181 | C2 | semidirect |
| 5. #31770850 | C2 | semidirect |
| 6. #31770833 | C2 | semidirect |
| 7. #31770641 | C2 | semidirect |
| 8. #31770615 | C2 | semidirect |
| 9. #418×C269 | C2 | semidirect |
| 16. C2×#16864385 | C22 | semidirect |
| 18. C2×C8×D269 | C22 | semidirect |
| 24. #22575433 | C22 | semidirect |
| 28. #22575386 | C22 | semidirect |
| 29. #22575384 | C22 | semidirect |
| 30. #22575378 | C22 | semidirect |
| 50. C2×#14524130 | D4 | semidirect |
| 120. C269 | #3057 | semidirect |
| 130. #418 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864390 | 2 |
| C2×#22575461 | 2 |
| #31771181 | 2 |
| #31771172 | 2 |
| #31770850 | 2 |
| #31770833 | 2 |
| #31770641 | 2 |
| #31770615 | 2 |
| #418×C269 | 2 |
| #3057 | 269 |