Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#16862361 | C2 | semidirect |
| 2. C2×#22554391 | C2 | semidirect |
| 3. #30681840 | C2 | semidirect |
| 4. #30681693 | C2 | semidirect |
| 5. C2×#127×C263 | C2 | semidirect |
| 22. C2×D1052 | D4 | semidirect |
| 27. C2×C263⋊C8 | D4 | semidirect |
| 66. C2×C4×C263 | D8 | semidirect |
| 97. C263 | #2011 | semidirect |
| 100. C2×#127 | D263 | semidirect |
| 163. 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×#22554391 | 2 |
| #30681840 | 2 |
| #30681693 | 2 |
| C2×#127×C263 | 2 |
| #2011 | 263 |