Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11718143 | C2 | semidirect |
| 16. #88178 | C4 | semidirect |
| 81. C22×C13 | #103 | semidirect |
| 139. C13 | #1892 | semidirect |
| 170. C22 | #88056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C13 | 2 |
| C2×#88178 | 2 |
| #11718873 | 2 |
| C2×#88056 | 2 |
| #11718143 | 2 |
| #1892 | 13 |