Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771333 | C2 | semidirect |
| 3. #31770955 | C2 | semidirect |
| 4. #31770912 | C2 | semidirect |
| 7. #31770812 | C2 | semidirect |
| 8. Q8×#14524130 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 115. C269 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771333 | 2 |
| #31770959 | 2 |
| #31770955 | 2 |
| #31770912 | 2 |
| #31770885 | 2 |
| #31770824 | 2 |
| #31770812 | 2 |
| Q8×#14524130 | 2 |
| C4×#16864392 | 2 |
| C4×#16864390 | 2 |
| #556×C269 | 2 |
| #3364 | 269 |