Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 3. #11719077 | C2 | semidirect |
| 4. #11719068 | C2 | semidirect |
| 5. #11719053 | C2 | semidirect |
| 6. #11719052 | C2 | semidirect |
| 7. C4×#6118 | C2 | semidirect |
| 22. #88112 | C22 | semidirect |
| 24. #88110 | C22 | semidirect |
| 25. C4⋊#1057 | C22 | semidirect |
| 26. C4×#1057 | C22 | semidirect |
| 160. C13 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#117 | 2 |
| #11719127 | 2 |
| #11719077 | 2 |
| #11719068 | 2 |
| #11719053 | 2 |
| #11719052 | 2 |
| C4×#6118 | 2 |
| #2921 | 13 |