Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#22575451 | C2 | semidirect |
| 4. #31770512 | C2 | semidirect |
| 5. #31770510 | C2 | semidirect |
| 6. #31770500 | C2 | semidirect |
| 7. #31770474 | C2 | semidirect |
| 36. C22×Dic269 | Q8 | semidirect |
| 99. C22×C269 | C4⋊Q8 | semidirect |
| 112. Dic269 | C22⋊Q8 | semidirect |
| 119. C269 | #2857 | semidirect |
| 219. C22 | #22575451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575451 | 2 |
| C2×#22575432 | 2 |
| C22×C4×Dic269 | 2 |
| #31770512 | 2 |
| #31770510 | 2 |
| #31770500 | 2 |
| #31770474 | 2 |
| #31770463 | 2 |
| C2×C22⋊Q8×C269 | 2 |
| #2857 | 269 |