Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31771410 | C2 | semidirect |
| 2. #31771043 | C2 | semidirect |
| 3. C2×D4304 | C2 | semidirect |
| 4. #31770875 | C2 | semidirect |
| 5. #31770419 | C2 | semidirect |
| 6. #31770413 | C2 | semidirect |
| 7. #350×C269 | C2 | semidirect |
| 16. C2×D2152 | C22 | semidirect |
| 20. #22575389 | C22 | semidirect |
| 23. M32×C269 | C22 | semidirect |
| 24. C2×C16×C269 | C22 | semidirect |
| 93. C269 | #2192 | semidirect |
| 101. #350 | D269 | semidirect |
| 115. M32 | C2×D269 | semidirect |
| 116. C2×C16 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771410 | 2 |
| #31771043 | 2 |
| C2×D4304 | 2 |
| #31770875 | 2 |
| #31770419 | 2 |
| #31770413 | 2 |
| #350×C269 | 2 |
| #2192 | 269 |