Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
272 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 17. #88055 | C4 | semidirect |
| 18. #88054 | C4 | semidirect |
| 66. #1055 | C4⋊C4 | semidirect |
| 129. C13 | #1771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88055 | 2 |
| C2×#88054 | 2 |
| C2×C8×Dic13 | 2 |
| C4×#6101 | 2 |
| C2×#88043 | 2 |
| C13×#336 | 2 |
| #11718142 | 2 |
| #1771 | 13 |