Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 4. C2×#88056 | C2 | semidirect |
| 5. C2×#88055 | C2 | semidirect |
| 6. #11718635 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 15. C2×#6105 | C4 | semidirect |
| 88. #1055 | C22⋊C4 | semidirect |
| 168. C13 | #1973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6105 | 2 |
| C2×C13×#102 | 2 |
| #11718882 | 2 |
| C2×#88056 | 2 |
| C2×#88055 | 2 |
| #11718635 | 2 |
| C2×#88047 | 2 |
| #1973 | 13 |