Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 5. #11718691 | C2 | semidirect |
| 6. C4×#6107 | C2 | semidirect |
| 17. C2×#6107 | C4 | semidirect |
| 161. C13 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#519 | 2 |
| C22×#6107 | 2 |
| #11719221 | 2 |
| #11718886 | 2 |
| #11718691 | 2 |
| C4×#6107 | 2 |
| #11718665 | 2 |
| #11718659 | 2 |
| #11718658 | 2 |
| #2950 | 13 |