Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
298 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 21. #88075 | C4 | semidirect |
| 59. Q8×C13 | C4⋊C4 | semidirect |
| 163. C13 | #1865 | semidirect |
| 168. Q8 | #6101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic13 | 2 |
| C2×C13×#103 | 2 |
| C2×#88075 | 2 |
| #11718634 | 2 |
| C2×#88048 | 2 |
| #11718143 | 2 |
| #11718142 | 2 |
| #1865 | 13 |