Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 59. #6107 | Q8 | semidirect |
| 181. C13 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| #11719272 | 2 |
| #11718755 | 2 |
| #11718739 | 2 |
| #11718725 | 2 |
| #11718724 | 2 |
| C4×#6107 | 2 |
| Q8×#1055 | 2 |
| #11718683 | 2 |
| #11718681 | 2 |
| #3383 | 13 |