Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#22575472 | C2 | semidirect |
| 2. #31771259 | C2 | semidirect |
| 3. #31770985 | C2 | semidirect |
| 4. #31770847 | C2 | semidirect |
| 5. #31770810 | C2 | semidirect |
| 6. #31770768 | C2 | semidirect |
| 7. C8×D1076 | C2 | semidirect |
| 8. C4×D8×C269 | C2 | semidirect |
| 49. D8×C269 | D4 | semidirect |
| 85. C4×C269 | #135 | semidirect |
| 95. C269 | #3283 | semidirect |
| 103. C4×D8 | D269 | semidirect |
| 137. D8 | D1076 | semidirect |
| 183. C4 | #22575472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575472 | 2 |
| #31771259 | 2 |
| #31770985 | 2 |
| #31770847 | 2 |
| #31770810 | 2 |
| #31770768 | 2 |
| C8×D1076 | 2 |
| C4×D8×C269 | 2 |
| #3283 | 269 |