Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#22575398 | C2 | semidirect |
| 3. #31770988 | C2 | semidirect |
| 4. #31770687 | C2 | semidirect |
| 5. #31770423 | C2 | semidirect |
| 6. #31770408 | C2 | semidirect |
| 7. #357×C269 | C2 | semidirect |
| 76. C269 | #2210 | semidirect |
| 84. #357 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575398 | 2 |
| C2×#22575394 | 2 |
| #31770988 | 2 |
| #31770687 | 2 |
| #31770423 | 2 |
| #31770408 | 2 |
| #357×C269 | 2 |
| #2210 | 269 |