Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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×#22575460 | C2 | semidirect |
| 2. #31771088 | C2 | semidirect |
| 3. #31770614 | C2 | semidirect |
| 4. #31770606 | C2 | semidirect |
| 5. #31770601 | C2 | semidirect |
| 6. C2×#22575377 | C2 | semidirect |
| 21. 2−1+4×C269 | C4 | semidirect |
| 40. #41×C269 | C2×C4 | semidirect |
| 45. C2×Q8×C269 | C2×C4 | semidirect |
| 94. C269 | #2898 | semidirect |
| 104. 2−1+4 | Dic269 | semidirect |
| 125. #41 | C2×Dic269 | semidirect |
| 130. C2×Q8 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #31771088 | 2 |
| #31770614 | 2 |
| #31770606 | 2 |
| #31770601 | 2 |
| C2×#22575377 | 2 |
| C2×2−1+4×C269 | 2 |
| #2898 | 269 |