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. #31770900 | C2 | semidirect |
| 3. #31770897 | C2 | semidirect |
| 5. #31770815 | C2 | semidirect |
| 6. #31770812 | C2 | semidirect |
| 78. C2×C4×C269 | Q16 | semidirect |
| 104. C269 | #3249 | semidirect |
| 182. C2×C4 | #16864392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31770900 | 2 |
| #31770897 | 2 |
| #31770844 | 2 |
| #31770815 | 2 |
| #31770812 | 2 |
| C2×C4⋊#14524130 | 2 |
| #533×C269 | 2 |
| #3249 | 269 |