Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #11719272 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 7. #11718514 | C2 | semidirect |
| 8. #11718454 | C2 | semidirect |
| 10. #11718360 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 195. C13 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719272 | 2 |
| #11719247 | 2 |
| C4×C13×SD16 | 2 |
| #11718828 | 2 |
| #11718692 | 2 |
| #11718680 | 2 |
| #11718514 | 2 |
| #11718454 | 2 |
| #11718428 | 2 |
| #11718360 | 2 |
| #11718340 | 2 |
| #3398 | 13 |