Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11719427 | C2 | semidirect |
| 4. #11718754 | C2 | semidirect |
| 6. #11718515 | C2 | semidirect |
| 7. #11718514 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 189. C13 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719427 | 2 |
| #11719247 | 2 |
| C13×#476 | 2 |
| #11718754 | 2 |
| C4×#6105 | 2 |
| #11718515 | 2 |
| #11718514 | 2 |
| #11718510 | 2 |
| #11718492 | 2 |
| #11718428 | 2 |
| #11718426 | 2 |
| #3369 | 13 |