Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #11718344 | C2 | semidirect |
| 3. C4×C13×C16 | C2 | semidirect |
| 5. #11718095 | C2 | semidirect |
| 43. C4×C16 | D13 | semidirect |
| 76. C13 | #2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718357 | 2 |
| #11718344 | 2 |
| C4×C13×C16 | 2 |
| #11718101 | 2 |
| #11718095 | 2 |
| #2242 | 13 |