Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 10. C2×C13×Q16 | C4 | semidirect |
| 11. C2×#6107 | C4 | semidirect |
| 14. C2×Dic52 | C4 | semidirect |
| 51. C2×#261 | Q16 | semidirect |
| 94. C2×Q16 | #261 | semidirect |
| 133. C13 | #1969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| (C2×#261)⋊Q8 | 2 |
| C2×#88117 | 2 |
| C2×#88102 | 2 |
| C2×C8×#261 | 2 |
| #1969 | 13 |