Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 12. #88124 | C4 | semidirect |
| 13. #88123 | C4 | semidirect |
| 14. #88123 | C4 | semidirect |
| 41. #6099 | Q8 | semidirect |
| 124. C13 | #1986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719175 | 2 |
| C4×C13×C4⋊C4 | 2 |
| C4×#6099 | 2 |
| #11718115 | 2 |
| #1986 | 13 |