Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22575484 | C2 | semidirect |
| 2. C2×#22575459 | C2 | semidirect |
| 4. #31771179 | C2 | semidirect |
| 5. #31770862 | C2 | semidirect |
| 6. #31770854 | C2 | semidirect |
| 7. #31770845 | C2 | semidirect |
| 8. #31770837 | C2 | semidirect |
| 9. #31770645 | C2 | semidirect |
| 10. #31770602 | C2 | semidirect |
| 11. C2×#103×C269 | C2 | semidirect |
| 58. #16864386 | D4 | semidirect |
| 143. C269 | #3063 | semidirect |
| 155. C2×#103 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C2×#22575459 | 2 |
| #31771186 | 2 |
| #31771179 | 2 |
| #31770862 | 2 |
| #31770854 | 2 |
| #31770845 | 2 |
| #31770837 | 2 |
| #31770645 | 2 |
| #31770602 | 2 |
| C2×#103×C269 | 2 |
| #3063 | 269 |