Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #31771040 | C2 | semidirect |
| 2. #31770982 | C2 | semidirect |
| 3. #31770426 | C2 | semidirect |
| 4. #31770417 | C2 | semidirect |
| 5. #443×C269 | C2 | semidirect |
| 25. Q16×C269 | D4 | semidirect |
| 27. D8×C269 | D4 | semidirect |
| 61. C269 | #2213 | semidirect |
| 65. #443 | D269 | semidirect |
| 82. Q16 | D1076 | semidirect |
| 88. D8 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771040 | 2 |
| #31770982 | 2 |
| #31770426 | 2 |
| #31770417 | 2 |
| #443×C269 | 2 |
| #2213 | 269 |