Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C4⋊(C263⋊C8) | C2 | semidirect |
| 3. C2×#22554391 | C2 | semidirect |
| 4. C2×#22554390 | C2 | semidirect |
| 5. #30681840 | C2 | semidirect |
| 6. #30681700 | C2 | semidirect |
| 7. #390×C263 | C2 | semidirect |
| 97. C2×C4×C263 | D8 | semidirect |
| 142. C263 | #2054 | semidirect |
| 149. #390 | D263 | semidirect |
| 238. C2×C4 | #16862361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16862361 | 2 |
| C2×C4⋊(C263⋊C8) | 2 |
| C2×#22554391 | 2 |
| C2×#22554390 | 2 |
| #30681840 | 2 |
| #30681700 | 2 |
| #390×C263 | 2 |
| #2054 | 263 |