Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #31770500 | C2 | semidirect |
| 3. #31770499 | C2 | semidirect |
| 4. #31770493 | C2 | semidirect |
| 5. #31770489 | C2 | semidirect |
| 7. #31770477 | C2 | semidirect |
| 8. #31770463 | C2 | semidirect |
| 12. #22575434 | C4 | semidirect |
| 36. C22×Dic269 | C2×C4 | semidirect |
| 44. #16864381 | C2×C4 | semidirect |
| 48. C22⋊Dic269 | C2×C4 | semidirect |
| 126. C269 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575434 | 2 |
| #31770500 | 2 |
| #31770499 | 2 |
| #31770493 | 2 |
| #31770489 | 2 |
| #31770485 | 2 |
| #31770477 | 2 |
| #31770463 | 2 |
| #390×C269 | 2 |
| #2376 | 269 |