Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22575451 | C2 | semidirect |
| 4. #31770813 | C2 | semidirect |
| 5. #31770808 | C2 | semidirect |
| 6. #31770628 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 8. #31770614 | C2 | semidirect |
| 116. Dic269 | #137 | semidirect |
| 121. C269 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575483 | 2 |
| C2×#22575451 | 2 |
| #41×Dic269 | 2 |
| #31770813 | 2 |
| #31770808 | 2 |
| #31770628 | 2 |
| #31770615 | 2 |
| #31770614 | 2 |
| C2×#137×C269 | 2 |
| #3039 | 269 |