Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31770909 | C2 | semidirect |
| 4. #31770812 | C2 | semidirect |
| 6. #31770710 | C2 | semidirect |
| 7. C4×#16864392 | C2 | semidirect |
| 95. C269 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771082 | 2 |
| #31770943 | 2 |
| #31770909 | 2 |
| #31770812 | 2 |
| #31770760 | 2 |
| #31770710 | 2 |
| C4×#16864392 | 2 |
| #31770666 | 2 |
| #541×C269 | 2 |
| #3127 | 269 |