Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771335 | C2 | semidirect |
| 3. #31770950 | C2 | semidirect |
| 4. #31770893 | C2 | semidirect |
| 5. #31770892 | C2 | semidirect |
| 6. #31770804 | C2 | semidirect |
| 7. #31770802 | C2 | semidirect |
| 8. C8×Dic538 | C2 | semidirect |
| 9. #31770696 | C2 | semidirect |
| 10. C4×#16864391 | C2 | semidirect |
| 11. #486×C269 | C2 | semidirect |
| 77. Dic538 | SD16 | semidirect |
| 78. Dic538 | #41 | semidirect |
| 125. C269 | #3362 | semidirect |
| 130. #486 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771335 | 2 |
| #31771275 | 2 |
| #31770950 | 2 |
| #31770893 | 2 |
| #31770892 | 2 |
| #31770804 | 2 |
| #31770802 | 2 |
| C8×Dic538 | 2 |
| #31770696 | 2 |
| C4×#16864391 | 2 |
| #486×C269 | 2 |
| #3362 | 269 |