Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 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×#432 | C2 | semidirect |
| 3. #11718593 | C2 | semidirect |
| 4. #11718062 | C2 | semidirect |
| 11. #88128 | C4 | semidirect |
| 13. C4×D52 | C4 | semidirect |
| 14. #88123 | C4 | semidirect |
| 65. #432 | D13 | semidirect |
| 124. C13 | #1505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719182 | 2 |
| C13×#432 | 2 |
| #11718593 | 2 |
| #11718062 | 2 |
| #1505 | 13 |