Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
316 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 77 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. #31770569 | C2 | semidirect |
| 3. #31770330 | C2 | semidirect |
| 4. #31770328 | C2 | semidirect |
| 5. #407×C269 | C2 | semidirect |
| 58. C22×D269 | M16 | semidirect |
| 67. C2×Dic269 | M16 | semidirect |
| 122. C269 | #1465 | semidirect |
| 126. #407 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D269 | 2 |
| #31770569 | 2 |
| #31770330 | 2 |
| #31770328 | 2 |
| #407×C269 | 2 |
| #1465 | 269 |