Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 123. C13 | #2090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718782 | 2 |
| #11718780 | 2 |
| #11718625 | 2 |
| C2×#88048 | 2 |
| C13×#343 | 2 |
| #11718150 | 2 |
| #11718146 | 2 |
| #2090 | 13 |