Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771328 | C2 | semidirect |
| 3. #31770952 | C2 | semidirect |
| 4. #31770932 | C2 | semidirect |
| 5. #31770890 | C2 | semidirect |
| 6. #31770837 | C2 | semidirect |
| 7. #31770805 | C2 | semidirect |
| 8. #31770766 | C2 | semidirect |
| 9. C8×D1076 | C2 | semidirect |
| 10. #31770600 | C2 | semidirect |
| 11. C4×Q16×C269 | C2 | semidirect |
| 127. C269 | #3304 | semidirect |
| 137. C4×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31771277 | 2 |
| #31770952 | 2 |
| #31770932 | 2 |
| #31770890 | 2 |
| #31770837 | 2 |
| #31770805 | 2 |
| #31770766 | 2 |
| C8×D1076 | 2 |
| #31770600 | 2 |
| C4×Q16×C269 | 2 |
| #3304 | 269 |