Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11718692 | C2 | semidirect |
| 5. #11718691 | C2 | semidirect |
| 6. C4×#6107 | C2 | semidirect |
| 7. #11718683 | C2 | semidirect |
| 158. C13 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#519 | 2 |
| #11719223 | 2 |
| #11718889 | 2 |
| #11718692 | 2 |
| #11718691 | 2 |
| C4×#6107 | 2 |
| #11718683 | 2 |
| #11718661 | 2 |
| #11718657 | 2 |
| #3127 | 13 |