Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. C13×#423 | C2 | semidirect |
| 4. #11718585 | C2 | semidirect |
| 5. #11718146 | C2 | semidirect |
| 81. #423 | D13 | semidirect |
| 97. C4×C13 | #100 | semidirect |
| 153. C13 | #1800 | semidirect |
| 196. C4 | #88063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C13×#423 | 2 |
| C2×#88063 | 2 |
| #11718585 | 2 |
| #11718146 | 2 |
| #1800 | 13 |