Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#88144 | C2 | semidirect |
| 5. C13×#340 | C2 | semidirect |
| 6. #11718142 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 95. #340 | D13 | semidirect |
| 174. C13 | #2025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88144 | 2 |
| C2×#88061 | 2 |
| #11718649 | 2 |
| C2×#88049 | 2 |
| C13×#340 | 2 |
| #11718142 | 2 |
| #11718121 | 2 |
| #2025 | 13 |