Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22575473 | C2 | semidirect |
| 2. #31771276 | C2 | semidirect |
| 3. #31770979 | C2 | semidirect |
| 4. #31770836 | C2 | semidirect |
| 5. #31770812 | C2 | semidirect |
| 6. #31770800 | C2 | semidirect |
| 7. #31770765 | C2 | semidirect |
| 8. #31770750 | C2 | semidirect |
| 9. C4×#16864390 | C2 | semidirect |
| 10. D4×#14524130 | C2 | semidirect |
| 11. #547×C269 | C2 | semidirect |
| 52. #16864390 | D4 | semidirect |
| 129. C4×C269 | #135 | semidirect |
| 140. C269 | #3284 | semidirect |
| 144. #547 | D269 | semidirect |
| 272. C4 | #22575473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575473 | 2 |
| #31771276 | 2 |
| #31770979 | 2 |
| #31770836 | 2 |
| #31770812 | 2 |
| #31770800 | 2 |
| #31770765 | 2 |
| #31770750 | 2 |
| C4×#16864390 | 2 |
| D4×#14524130 | 2 |
| #547×C269 | 2 |
| #3284 | 269 |