Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #11718535 | C2 | semidirect |
| 3. C13×#367 | C2 | semidirect |
| 5. #11718093 | C2 | semidirect |
| 7. #11718082 | C2 | semidirect |
| 31. D104 | Q8 | semidirect |
| 52. #367 | D13 | semidirect |
| 97. C13 | #2226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718535 | 2 |
| #11718533 | 2 |
| C13×#367 | 2 |
| #11718101 | 2 |
| #11718093 | 2 |
| #11718083 | 2 |
| #11718082 | 2 |
| #2226 | 13 |