Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 4. #31770813 | C2 | direct (N × H) |
| 72. C2×Dic269 | Q16 | semidirect |
| 104. Dic269 | C2×Q16 | semidirect |
| 105. C2×C269 | #462 | semidirect |
| 109. C269 | C2×#462 | semidirect |
| 215. C2 | #31770813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864392 | 2 |
| C2×#22575451 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770813 | 2 |
| C2×#22575382 | 2 |
| C2×#22575378 | 2 |
| C2×#22575377 | 2 |
| C22×Q16×C269 | 2 |
| C2×#462 | 269 |