Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. #31771043 | C2 | semidirect |
| 2. #31770982 | C2 | semidirect |
| 3. #31770723 | C2 | semidirect |
| 4. #31770419 | C2 | semidirect |
| 5. #364×C269 | C2 | semidirect |
| 20. Dic1076 | D4 | semidirect |
| 26. D2152 | D4 | semidirect |
| 61. C269 | #2213 | semidirect |
| 66. #364 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771043 | 2 |
| #31770982 | 2 |
| #31770723 | 2 |
| #31770419 | 2 |
| #364×C269 | 2 |
| #2213 | 269 |