Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 148 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. #11719146 | C2 | semidirect |
| 3. #11719145 | C2 | semidirect |
| 4. #11719144 | C2 | semidirect |
| 5. D4×#1057 | C2 | semidirect |
| 6. #11719054 | C2 | semidirect |
| 7. #11719049 | C2 | semidirect |
| 143. C13 | #2981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11719146 | 2 |
| #11719145 | 2 |
| #11719144 | 2 |
| D4×#1057 | 2 |
| #11719054 | 2 |
| #11719049 | 2 |
| #2981 | 13 |