Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
416 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #31770898 | C2 | direct (N × H) |
| 48. C2×Q8×C269 | Q8 | semidirect |
| 70. Q8×C269 | C2×Q8 | semidirect |
| 93. C2×C269 | #477 | semidirect |
| 97. C269 | C2×#477 | semidirect |
| 131. C2×Q8 | Dic538 | semidirect |
| 159. Q8 | C2×Dic538 | semidirect |
| 191. C2 | #31770898 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575452 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770898 | 2 |
| C2×#22575387 | 2 |
| C2×#22575386 | 2 |
| C2×#22575382 | 2 |
| C2×#22575377 | 2 |
| C2×#103×C269 | 2 |
| C2×#477 | 269 |