Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #31770561 | C2 | semidirect |
| 3. C4×#16864386 | C2 | semidirect |
| 4. C2×#22575364 | C2 | semidirect |
| 6. #22575460 | C4 | semidirect |
| 18. #16864386 | C2×C4 | semidirect |
| 19. C2×#14524130 | C2×C4 | semidirect |
| 53. C269 | #2875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #31770561 | 2 |
| C4×#16864386 | 2 |
| C2×#22575364 | 2 |
| C4×#41×C269 | 2 |
| #2875 | 269 |