Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575475 | C2 | semidirect |
| 2. C2×#22575459 | C2 | semidirect |
| 3. #31771186 | C2 | semidirect |
| 4. #31770864 | C2 | semidirect |
| 5. #31770859 | C2 | semidirect |
| 6. #31770835 | C2 | semidirect |
| 7. #31770604 | C2 | semidirect |
| 8. C2×#106×C269 | C2 | semidirect |
| 55. C2×C8×C269 | D4 | semidirect |
| 105. C269 | #3060 | semidirect |
| 113. C2×#106 | D269 | semidirect |
| 158. C2×C8 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| C2×#22575459 | 2 |
| #31771186 | 2 |
| #31770864 | 2 |
| #31770859 | 2 |
| #31770835 | 2 |
| #31770604 | 2 |
| C2×#106×C269 | 2 |
| #3060 | 269 |