Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 8. #11718450 | C2 | direct (N × H) |
| 15. C2×#6107 | C4 | semidirect |
| 49. #6107 | C2×C4 | semidirect |
| 128. C2×C13 | #441 | semidirect |
| 162. C13 | C2×#441 | semidirect |
| 201. C2 | #11718450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic13 | 2 |
| C22×#6107 | 2 |
| C2×#88141 | 2 |
| C2×C13×#103 | 2 |
| C2×#88056 | 2 |
| C2×#88055 | 2 |
| C2×#88048 | 2 |
| #11718450 | 2 |
| C2×#441 | 13 |