Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C2×#88062 | C2 | semidirect |
| 5. C2×#88047 | C2 | semidirect |
| 6. #11718146 | C2 | semidirect |
| 7. #11718122 | C2 | semidirect |
| 12. #88202 | C4 | semidirect |
| 159. C13 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88202 | 2 |
| C13×#417 | 2 |
| #11718893 | 2 |
| C2×#88062 | 2 |
| C2×#88047 | 2 |
| #11718146 | 2 |
| #11718122 | 2 |
| #1816 | 13 |