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×#22575474 | C2 | semidirect |
| 2. #31771156 | C2 | semidirect |
| 3. #31771153 | C2 | semidirect |
| 4. #31770986 | C2 | semidirect |
| 5. #31770984 | C2 | semidirect |
| 6. #31770981 | C2 | semidirect |
| 7. #31770978 | C2 | semidirect |
| 8. C4×C8×D269 | C2 | semidirect |
| 9. #492×C269 | C2 | semidirect |
| 47. C8×D269 | D4 | semidirect |
| 91. C4×C269 | #135 | semidirect |
| 101. C269 | #3147 | semidirect |
| 110. #492 | D269 | semidirect |
| 196. C4 | #22575474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575474 | 2 |
| #31771156 | 2 |
| #31771153 | 2 |
| #31770986 | 2 |
| #31770984 | 2 |
| #31770981 | 2 |
| #31770978 | 2 |
| C4×C8×D269 | 2 |
| #492×C269 | 2 |
| #3147 | 269 |