Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #31770901 | C2 | semidirect |
| 4. #31770816 | C2 | semidirect |
| 47. C2×C4×C269 | Q16 | semidirect |
| 68. C269 | #3249 | semidirect |
| 116. C2×C4 | Dic1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31770901 | 2 |
| #31770846 | 2 |
| #31770816 | 2 |
| C2×C4⋊C8×C269 | 2 |
| #3249 | 269 |