Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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. #88102 | C4 | semidirect |
| 10. #88101 | C4 | semidirect |
| 11. C13×M32 | C4 | semidirect |
| 12. #88052 | C4 | semidirect |
| 63. M32 | #261 | semidirect |
| 88. C13 | #1386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719092 | 2 |
| C2×#88101 | 2 |
| D13×M32 | 2 |
| #1386 | 13 |