Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575476 | C2 | semidirect |
| 2. C2×#22575474 | C2 | semidirect |
| 3. C2×#22575472 | C2 | semidirect |
| 4. #31771154 | C2 | semidirect |
| 5. #31770989 | C2 | semidirect |
| 6. #31770987 | C2 | semidirect |
| 7. #31770983 | C2 | semidirect |
| 8. #31770980 | C2 | semidirect |
| 9. #31770976 | C2 | semidirect |
| 10. C4×C8×D269 | C2 | semidirect |
| 11. #495×C269 | C2 | semidirect |
| 62. C8×D269 | D4 | semidirect |
| 63. C8×D269 | D4 | semidirect |
| 119. Dic269 | #135 | semidirect |
| 125. C269 | #3147 | semidirect |
| 133. #495 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×#22575474 | 2 |
| C2×#22575472 | 2 |
| #31771154 | 2 |
| #31770989 | 2 |
| #31770987 | 2 |
| #31770983 | 2 |
| #31770980 | 2 |
| #31770976 | 2 |
| C4×C8×D269 | 2 |
| #495×C269 | 2 |
| #3147 | 269 |