Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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×#88055 | C2 | semidirect |
| 4. #11718646 | C2 | semidirect |
| 6. C13×#340 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 21. #88049 | C4 | semidirect |
| 94. #340 | D13 | semidirect |
| 170. C13 | #1936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88061 | 2 |
| C2×#88055 | 2 |
| #11718649 | 2 |
| #11718646 | 2 |
| C2×#88049 | 2 |
| C13×#340 | 2 |
| #11718121 | 2 |
| #1936 | 13 |