Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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×#544 | C2 | semidirect |
| 3. #11718752 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718727 | C2 | semidirect |
| 6. #11718724 | C2 | semidirect |
| 8. #11718660 | C2 | semidirect |
| 9. #11718656 | C2 | semidirect |
| 11. C2×#88047 | C2 | semidirect |
| 47. #6127 | Q8 | semidirect |
| 102. #544 | D13 | semidirect |
| 198. C13 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#544 | 2 |
| #11719228 | 2 |
| #11718752 | 2 |
| #11718748 | 2 |
| #11718727 | 2 |
| #11718724 | 2 |
| #11718663 | 2 |
| #11718660 | 2 |
| #11718656 | 2 |
| #11718627 | 2 |
| C2×#88047 | 2 |
| #3083 | 13 |