Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #11719426 | C2 | semidirect |
| 3. C13×#462 | C2 | semidirect |
| 4. #11718851 | C2 | semidirect |
| 5. #11718846 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 10. #11718479 | C2 | semidirect |
| 11. #11718478 | C2 | semidirect |
| 108. #462 | D13 | semidirect |
| 197. C13 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719426 | 2 |
| #11719290 | 2 |
| C13×#462 | 2 |
| #11718851 | 2 |
| #11718846 | 2 |
| #11718746 | 2 |
| C4×#6107 | 2 |
| #11718509 | 2 |
| #11718492 | 2 |
| #11718479 | 2 |
| #11718478 | 2 |
| #3400 | 13 |