Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #31770356 | C2 | semidirect |
| 4. #31770355 | C2 | semidirect |
| 5. #334×C269 | C2 | semidirect |
| 43. #14524130 | M16 | semidirect |
| 49. C8×C269 | M16 | semidirect |
| 65. C269 | #1566 | semidirect |
| 71. #334 | D269 | semidirect |
| 115. C8 | #16864385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770627 | 2 |
| C4×C8×D269 | 2 |
| #31770356 | 2 |
| #31770355 | 2 |
| #334×C269 | 2 |
| #1566 | 269 |