Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic538 | C2 | semidirect |
| 3. #31770956 | C2 | semidirect |
| 4. #31770936 | C2 | semidirect |
| 5. #31770891 | C2 | semidirect |
| 6. #31770834 | C2 | semidirect |
| 7. #31770811 | C2 | semidirect |
| 8. #31770746 | C2 | semidirect |
| 9. C4×#16864391 | C2 | semidirect |
| 10. C2×#22575378 | C2 | semidirect |
| 11. C8×D4×C269 | C2 | semidirect |
| 83. Dic538 | #41 | semidirect |
| 96. D4×C269 | SD16 | semidirect |
| 128. C269 | #3298 | semidirect |
| 139. C8×D4 | D269 | semidirect |
| 217. D4 | #16864391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic538 | 2 |
| #31771259 | 2 |
| #31770956 | 2 |
| #31770936 | 2 |
| #31770891 | 2 |
| #31770834 | 2 |
| #31770811 | 2 |
| #31770746 | 2 |
| C4×#16864391 | 2 |
| C2×#22575378 | 2 |
| C8×D4×C269 | 2 |
| #3298 | 269 |