Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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. #31771372 | C2 | semidirect |
| 2. #31770622 | C2 | semidirect |
| 3. #31770610 | C2 | semidirect |
| 4. C2×#22575370 | C2 | semidirect |
| 5. #31770376 | C2 | semidirect |
| 6. #31770363 | C2 | semidirect |
| 22. C2×SD16×C269 | C4 | semidirect |
| 23. C2×D8×C269 | C4 | semidirect |
| 112. C269 | #1903 | semidirect |
| 125. C2×SD16 | Dic269 | semidirect |
| 126. C2×D8 | Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771372 | 2 |
| #31770622 | 2 |
| #31770610 | 2 |
| C2×#22575370 | 2 |
| #31770376 | 2 |
| #31770363 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #1903 | 269 |