Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 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. C2×Q8×Dic269 | C2 | semidirect |
| 5. #31770494 | C2 | semidirect |
| 6. #31770479 | C2 | semidirect |
| 7. #31770474 | C2 | semidirect |
| 8. #31770451 | C2 | semidirect |
| 9. #391×C269 | C2 | semidirect |
| 12. #22575442 | C4 | semidirect |
| 45. #16864379 | C2×C4 | semidirect |
| 47. C4×Dic269 | C2×C4 | semidirect |
| 51. C2×Q8×C269 | C2×C4 | semidirect |
| 111. C269 | #2326 | semidirect |
| 116. #391 | D269 | semidirect |
| 145. C2×Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575442 | 2 |
| C2×Q8×Dic269 | 2 |
| C2×#22575415 | 2 |
| #31770507 | 2 |
| #31770494 | 2 |
| #31770479 | 2 |
| #31770474 | 2 |
| #31770451 | 2 |
| #391×C269 | 2 |
| #2326 | 269 |