Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. C13×#550 | C2 | semidirect |
| 2. #11719284 | C2 | semidirect |
| 3. #11718733 | C2 | semidirect |
| 4. #11718733 | C2 | semidirect |
| 5. #11718732 | C2 | semidirect |
| 6. #11718731 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 8. #11718675 | C2 | semidirect |
| 9. C4×#6104 | C2 | semidirect |
| 10. #11718670 | C2 | semidirect |
| 11. #11718669 | C2 | semidirect |
| 98. D52 | #41 | semidirect |
| 106. #550 | D13 | semidirect |
| 203. C13 | #3366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| #11719284 | 2 |
| #11718733 | 2 |
| #11718732 | 2 |
| #11718731 | 2 |
| #11718685 | 2 |
| #11718675 | 2 |
| C4×#6104 | 2 |
| #11718670 | 2 |
| #11718669 | 2 |
| #3366 | 13 |