Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #11719228 | C2 | semidirect |
| 3. C13×#428 | C2 | semidirect |
| 4. #11718794 | C2 | semidirect |
| 5. #11718790 | C2 | semidirect |
| 6. #11718663 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718545 | C2 | semidirect |
| 9. #11718543 | C2 | semidirect |
| 10. #11718528 | C2 | semidirect |
| 11. #11718527 | C2 | semidirect |
| 115. #428 | D13 | semidirect |
| 210. C13 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719228 | 2 |
| #11719215 | 2 |
| C13×#428 | 2 |
| #11718794 | 2 |
| #11718790 | 2 |
| #11718663 | 2 |
| C2×#88047 | 2 |
| #11718545 | 2 |
| #11718543 | 2 |
| #11718528 | 2 |
| #11718527 | 2 |
| #3098 | 13 |