Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 19. #88043 | C4 | semidirect |
| 20. C4×#1055 | C4 | semidirect |
| 124. C13 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88062 | 2 |
| #11718659 | 2 |
| #11718658 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #11718151 | 2 |
| #11718125 | 2 |
| #11718123 | 2 |
| #1833 | 13 |