Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 2. #31770659 | C2 | semidirect |
| 3. #31770655 | C2 | semidirect |
| 4. #31770628 | C2 | semidirect |
| 6. M16×Dic269 | C2 | semidirect |
| 17. #22575382 | C22 | semidirect |
| 19. #22575363 | C22 | semidirect |
| 20. C8×Dic269 | C22 | semidirect |
| 56. C2×Dic269 | M16 | semidirect |
| 92. C269 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic269 | 2 |
| #31770659 | 2 |
| #31770655 | 2 |
| #31770628 | 2 |
| #31770569 | 2 |
| M16×Dic269 | 2 |
| #407×C269 | 2 |
| #2920 | 269 |