Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. C13×#554 | C2 | semidirect |
| 2. #11719282 | C2 | semidirect |
| 3. #11718749 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718728 | C2 | semidirect |
| 6. #11718727 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 8. #11718676 | C2 | semidirect |
| 9. #11718676 | C2 | semidirect |
| 10. #11718675 | C2 | semidirect |
| 11. C4×#6104 | C2 | semidirect |
| 81. D4×C13 | #41 | semidirect |
| 105. #554 | D13 | semidirect |
| 203. C13 | #3366 | semidirect |
| 218. D4 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| #11719282 | 2 |
| #11718749 | 2 |
| #11718745 | 2 |
| #11718728 | 2 |
| #11718727 | 2 |
| #11718685 | 2 |
| #11718676 | 2 |
| #11718675 | 2 |
| C4×#6104 | 2 |
| #3366 | 13 |