Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 77. Dic538 | Q16 | semidirect |
| 112. C269 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic538 | 2 |
| #31771333 | 2 |
| #31770956 | 2 |
| #31770954 | 2 |
| #31770900 | 2 |
| #31770899 | 2 |
| #31770815 | 2 |
| #31770813 | 2 |
| C8×Dic538 | 2 |
| #31770697 | 2 |
| C4×Q16×C269 | 2 |
| #3363 | 269 |