Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31771013 | C2 | semidirect |
| 3. #31771011 | C2 | semidirect |
| 4. #31771009 | C2 | semidirect |
| 5. #31771007 | C2 | semidirect |
| 6. #31771006 | C2 | semidirect |
| 11. #500×C269 | C2 | semidirect |
| 42. #16864385 | Q8 | semidirect |
| 45. C8×D269 | Q8 | semidirect |
| 107. C269 | #3164 | semidirect |
| 113. #500 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771232 | 2 |
| #31771013 | 2 |
| #31771011 | 2 |
| #31771009 | 2 |
| #31771007 | 2 |
| #31771006 | 2 |
| #31770646 | 2 |
| #31770642 | 2 |
| #107×D269 | 2 |
| #31770559 | 2 |
| #500×C269 | 2 |
| #3164 | 269 |