Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. #11719158 | C2 | semidirect |
| 3. #11719075 | C2 | semidirect |
| 4. #11719073 | C2 | semidirect |
| 5. #11719055 | C2 | semidirect |
| 6. #11719054 | C2 | semidirect |
| 7. C4×#6118 | C2 | semidirect |
| 8. #11719047 | C2 | semidirect |
| 74. D52 | M16 | semidirect |
| 83. #1057 | #41 | semidirect |
| 164. C13 | #2970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6131 | 2 |
| #11719158 | 2 |
| #11719075 | 2 |
| #11719073 | 2 |
| #11719055 | 2 |
| #11719054 | 2 |
| C4×#6118 | 2 |
| #11719047 | 2 |
| #2970 | 13 |