Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic538 | C2 | semidirect |
| 4. #31770511 | C2 | semidirect |
| 6. #31770497 | C2 | semidirect |
| 7. #31770479 | C2 | semidirect |
| 8. #31770475 | C2 | semidirect |
| 9. #376×C269 | C2 | semidirect |
| 13. #22575441 | C4 | semidirect |
| 33. C2×Dic538 | C2×C4 | semidirect |
| 48. #16864379 | C2×C4 | semidirect |
| 56. C42×C269 | C2×C4 | semidirect |
| 111. C269 | #2326 | semidirect |
| 121. #376 | D269 | semidirect |
| 168. C42 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575441 | 2 |
| C2×C4×Dic538 | 2 |
| C2×C4×D1076 | 2 |
| #31770511 | 2 |
| #31770507 | 2 |
| #31770497 | 2 |
| #31770479 | 2 |
| #31770475 | 2 |
| #376×C269 | 2 |
| #2326 | 269 |