Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #31771008 | C2 | semidirect |
| 3. #31770815 | C2 | semidirect |
| 4. #31770351 | C2 | semidirect |
| 5. Q8⋊#14524130 | C2 | semidirect |
| 63. D4×C269 | Q16 | semidirect |
| 92. C269 | #1649 | semidirect |
| 152. D4 | #16864392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771008 | 2 |
| #31770885 | 2 |
| #31770815 | 2 |
| #31770351 | 2 |
| Q8⋊#14524130 | 2 |
| D4⋊#14524130 | 2 |
| D4×Q8×C269 | 2 |
| #1649 | 269 |