Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
396 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #30681961 | C2 | semidirect |
| 3. C2×#22554387 | C2 | semidirect |
| 4. C2×#22554386 | C2 | semidirect |
| 5. C2×#22554386 | C2 | semidirect |
| 6. M16×Dic263 | C2 | semidirect |
| 7. C2×#100×C263 | C2 | semidirect |
| 40. #16862360 | D4 | semidirect |
| 57. M16×C263 | D4 | semidirect |
| 109. Dic263 | #100 | semidirect |
| 116. C263 | #1965 | semidirect |
| 123. C2×#100 | D263 | semidirect |
| 169. M16 | C22⋊D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554466 | 2 |
| #30681961 | 2 |
| C2×#22554387 | 2 |
| C2×#22554386 | 2 |
| M16×Dic263 | 2 |
| C2×#100×C263 | 2 |
| #1965 | 263 |