Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #31771236 | C2 | semidirect |
| 3. #31770914 | C2 | semidirect |
| 4. #31770903 | C2 | semidirect |
| 5. #31770893 | C2 | semidirect |
| 6. #31770888 | C2 | semidirect |
| 7. #31770647 | C2 | semidirect |
| 8. C2×#22575384 | C2 | semidirect |
| 9. #31770633 | C2 | semidirect |
| 64. #41×C269 | Q8 | semidirect |
| 123. C269 | #3084 | semidirect |
| 166. #41 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771236 | 2 |
| #31771088 | 2 |
| #31770914 | 2 |
| #31770903 | 2 |
| #31770893 | 2 |
| #31770888 | 2 |
| #31770647 | 2 |
| C2×#22575384 | 2 |
| #31770633 | 2 |
| #31770601 | 2 |
| #417×C269 | 2 |
| #3084 | 269 |