Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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×#431 | C2 | semidirect |
| 3. #11718593 | C2 | semidirect |
| 5. #11718059 | C2 | semidirect |
| 13. #88129 | C4 | semidirect |
| 14. C4×D52 | C4 | semidirect |
| 16. #88124 | C4 | semidirect |
| 17. C4×Dic26 | C4 | semidirect |
| 73. #431 | D13 | semidirect |
| 142. C13 | #1500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| C13×#431 | 2 |
| #11718593 | 2 |
| #11718062 | 2 |
| #11718059 | 2 |
| #1500 | 13 |