Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#22575474 | C2 | semidirect |
| 2. #31771277 | C2 | semidirect |
| 3. #31771259 | C2 | semidirect |
| 4. #31770978 | C2 | semidirect |
| 5. #31770835 | C2 | semidirect |
| 6. #31770815 | C2 | semidirect |
| 7. #31770800 | C2 | semidirect |
| 8. #31770770 | C2 | semidirect |
| 9. #31770751 | C2 | semidirect |
| 10. C8×D1076 | C2 | semidirect |
| 11. C4×SD16×C269 | C2 | semidirect |
| 73. SD16×C269 | D4 | semidirect |
| 129. C4×C269 | #135 | semidirect |
| 140. C269 | #3284 | semidirect |
| 151. C4×SD16 | D269 | semidirect |
| 204. SD16 | D1076 | semidirect |
| 272. 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 |
| #31771277 | 2 |
| #31771259 | 2 |
| #31770978 | 2 |
| #31770835 | 2 |
| #31770815 | 2 |
| #31770800 | 2 |
| #31770770 | 2 |
| #31770751 | 2 |
| C8×D1076 | 2 |
| C4×SD16×C269 | 2 |
| #3284 | 269 |