Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. C13×#427 | C2 | semidirect |
| 3. C2×#88052 | C2 | semidirect |
| 4. #11718080 | C2 | semidirect |
| 8. C2×Dic52 | C4 | semidirect |
| 11. #88158 | C4 | semidirect |
| 13. C2×D104 | C4 | semidirect |
| 16. C13×#106 | C22 | semidirect |
| 18. #88052 | C22 | semidirect |
| 70. #427 | D13 | semidirect |
| 98. #106 | C2×D13 | semidirect |
| 129. C13 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| C13×#427 | 2 |
| C2×#88052 | 2 |
| #11718080 | 2 |
| #2145 | 13 |