Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #31770955 | C2 | semidirect |
| 3. #31770933 | C2 | semidirect |
| 4. #31770890 | C2 | semidirect |
| 5. #31770836 | C2 | semidirect |
| 6. #31770807 | C2 | semidirect |
| 7. #31770744 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. C2×#22575377 | C2 | semidirect |
| 11. D4×Q8×C269 | C2 | semidirect |
| 94. Q8×C269 | #41 | semidirect |
| 95. D4×C269 | SD16 | semidirect |
| 128. C269 | #3298 | semidirect |
| 130. D4×Q8 | D269 | semidirect |
| 213. Q8 | #16864401 | semidirect |
| 217. D4 | #16864389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771259 | 2 |
| #31770955 | 2 |
| #31770933 | 2 |
| #31770890 | 2 |
| #31770836 | 2 |
| #31770807 | 2 |
| #31770744 | 2 |
| C4×#16864389 | 2 |
| D4×#14524130 | 2 |
| C2×#22575377 | 2 |
| D4×Q8×C269 | 2 |
| #3298 | 269 |