Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719224 | C2 | semidirect |
| 3. C13×#428 | C2 | semidirect |
| 5. #11718780 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718551 | C2 | semidirect |
| 9. #11718536 | C2 | semidirect |
| 10. #11718532 | C2 | semidirect |
| 11. #11718518 | C2 | semidirect |
| 46. #6127 | Q8 | semidirect |
| 108. #428 | 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 |
|---|---|
| #11719224 | 2 |
| #11719209 | 2 |
| C13×#428 | 2 |
| #11718794 | 2 |
| #11718780 | 2 |
| #11718663 | 2 |
| C2×#88047 | 2 |
| #11718551 | 2 |
| #11718536 | 2 |
| #11718532 | 2 |
| #11718518 | 2 |
| #3083 | 13 |