Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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. #31770683 | C2 | semidirect |
| 2. #31770677 | C2 | semidirect |
| 3. #31770666 | C2 | semidirect |
| 4. #31770572 | C2 | semidirect |
| 5. #31770569 | C2 | semidirect |
| 8. C2×#16864386 | C22 | semidirect |
| 9. C22×#14524130 | C22 | semidirect |
| 10. C4⋊#14524130 | C22 | semidirect |
| 14. C22⋊#14524130 | C22 | semidirect |
| 15. #22575364 | C22 | semidirect |
| 16. C4×#14524130 | C22 | semidirect |
| 89. C269 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770683 | 2 |
| #31770677 | 2 |
| #31770666 | 2 |
| #31770572 | 2 |
| #31770569 | 2 |
| #525×C269 | 2 |
| #2978 | 269 |