Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 3. C2×#88064 | C2 | semidirect |
| 4. C2×#88050 | C2 | semidirect |
| 6. C13×#343 | C2 | semidirect |
| 7. #11718150 | C2 | semidirect |
| 16. #88163 | C4 | semidirect |
| 101. #343 | D13 | semidirect |
| 180. C13 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| C2×#88161 | 2 |
| C2×#88064 | 2 |
| C2×#88050 | 2 |
| #11718627 | 2 |
| C13×#343 | 2 |
| #11718150 | 2 |
| #1908 | 13 |