Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
652 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#22575410 | C2 | semidirect |
| 4. #31770503 | C2 | semidirect |
| 5. #31770496 | C2 | semidirect |
| 6. C4×C4⋊Dic269 | C2 | semidirect |
| 7. C4×#16864379 | C2 | semidirect |
| 8. C43×C269 | C2 | semidirect |
| 11. C4×D1076 | C4 | semidirect |
| 51. C42×C269 | D4 | semidirect |
| 92. C4×C269 | #117 | semidirect |
| 102. C269 | #2293 | semidirect |
| 111. C43 | D269 | semidirect |
| 154. C42 | D1076 | semidirect |
| 197. C4 | #22575410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1076 | 2 |
| C2×#22575410 | 2 |
| #31770507 | 2 |
| #31770503 | 2 |
| #31770496 | 2 |
| C4×C4⋊Dic269 | 2 |
| C4×#16864379 | 2 |
| C43×C269 | 2 |
| #2293 | 269 |