Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22575476 | C2 | semidirect |
| 2. #31771156 | C2 | semidirect |
| 3. #31770990 | C2 | semidirect |
| 4. #31770982 | C2 | semidirect |
| 5. #31770979 | C2 | semidirect |
| 6. C4×C8×D269 | C2 | semidirect |
| 7. #494×C269 | C2 | semidirect |
| 33. C8×D269 | D4 | semidirect |
| 64. C4×C269 | #135 | semidirect |
| 72. C269 | #3147 | semidirect |
| 77. #494 | D269 | semidirect |
| 139. C4 | #22575476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| #31771156 | 2 |
| #31770990 | 2 |
| #31770982 | 2 |
| #31770979 | 2 |
| C4×C8×D269 | 2 |
| #494×C269 | 2 |
| #3147 | 269 |