Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
340 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22554404 | C2 | semidirect |
| 3. C2×#22554395 | C2 | semidirect |
| 5. #30681844 | C2 | semidirect |
| 7. C2×#97×C263 | C2 | semidirect |
| 12. C2×#16862365 | C4 | semidirect |
| 87. C8×C263 | C22⋊C4 | semidirect |
| 112. C263 | #1973 | semidirect |
| 118. C2×#97 | D263 | semidirect |
| 200. C8 | (C2×D263)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16862365 | 2 |
| C2×#22554404 | 2 |
| C2×#22554395 | 2 |
| C2×#22554392 | 2 |
| #30681844 | 2 |
| #30681840 | 2 |
| C2×#97×C263 | 2 |
| #1973 | 263 |