Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 1. C2×#22554469 | C2 | semidirect |
| 5. #30681700 | C2 | semidirect |
| 6. #30681692 | C2 | semidirect |
| 7. #340×C263 | C2 | semidirect |
| 32. C2×D1052 | Q8 | semidirect |
| 123. C263 | #2023 | semidirect |
| 130. #340 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22554469 | 2 |
| C2×#22554392 | 2 |
| C2×#22554390 | 2 |
| #30681839 | 2 |
| #30681700 | 2 |
| #30681692 | 2 |
| #340×C263 | 2 |
| #2023 | 263 |