Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#16864403 | C2 | semidirect |
| 3. #31770718 | C2 | semidirect |
| 4. #31770716 | C2 | semidirect |
| 5. #31770712 | C2 | semidirect |
| 6. #31770708 | C2 | semidirect |
| 7. #31770703 | C2 | semidirect |
| 8. #31770640 | C2 | semidirect |
| 9. #31770600 | C2 | semidirect |
| 10. #97×D269 | C2 | semidirect |
| 11. #441×C269 | C2 | semidirect |
| 13. #22575476 | C4 | semidirect |
| 41. #16864403 | C2×C4 | semidirect |
| 49. #16864389 | C2×C4 | semidirect |
| 50. D2152 | C2×C4 | semidirect |
| 54. C8×D269 | C2×C4 | semidirect |
| 65. Q16×C269 | C2×C4 | semidirect |
| 114. C269 | #2943 | semidirect |
| 121. #441 | D269 | semidirect |
| 165. Q16 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C4×#16864403 | 2 |
| #31770718 | 2 |
| #31770716 | 2 |
| #31770712 | 2 |
| #31770708 | 2 |
| #31770703 | 2 |
| #31770640 | 2 |
| #31770600 | 2 |
| #97×D269 | 2 |
| #441×C269 | 2 |
| #2943 | 269 |