Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 7. C13×C4⋊Q8 | C4 | semidirect |
| 9. Q8×Dic13 | C4 | semidirect |
| 15. #88123 | C4 | semidirect |
| 80. C4⋊Q8 | #261 | semidirect |
| 120. C13 | #1503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| C4×C4⋊#261 | 2 |
| #11719051 | 2 |
| #11718298 | 2 |
| #1503 | 13 |