Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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. #30681710 | C2 | semidirect |
| 5. #30681709 | C2 | semidirect |
| 6. #30681708 | C2 | semidirect |
| 7. #344×C263 | C2 | semidirect |
| 89. C263 | #1829 | semidirect |
| 97. #344 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30682412 | 2 |
| C2×#22554386 | 2 |
| #30681710 | 2 |
| #30681709 | 2 |
| #30681708 | 2 |
| #344×C263 | 2 |
| #1829 | 263 |