Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #31770463 | C2 | semidirect |
| 4. #31770371 | C2 | semidirect |
| 6. C23×Dic269 | C4 | semidirect |
| 10. C2×C4⋊Dic269 | C4 | semidirect |
| 12. C2×C22⋊Dic269 | C4 | semidirect |
| 15. C2×C4×Dic269 | C4 | semidirect |
| 72. C23×C269 | C4⋊C4 | semidirect |
| 85. C2×C4×C269 | C4⋊C4 | semidirect |
| 110. Dic269 | #99 | semidirect |
| 119. C269 | #1799 | semidirect |
| 176. C23 | #16864381 | semidirect |
| 205. C2×C4 | #16864381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic269 | 2 |
| C2×#22575368 | 2 |
| #31770463 | 2 |
| #31770371 | 2 |
| C2×#99×C269 | 2 |
| #1799 | 269 |