Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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×#88064 | C2 | semidirect |
| 5. #11718786 | C2 | semidirect |
| 6. #11718665 | C2 | semidirect |
| 7. #11718125 | C2 | semidirect |
| 163. C13 | #2049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88205 | 2 |
| C13×#421 | 2 |
| #11718898 | 2 |
| C2×#88064 | 2 |
| #11718786 | 2 |
| #11718665 | 2 |
| #11718125 | 2 |
| #2049 | 13 |