Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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×#405 | C2 | semidirect |
| 3. C2×#88064 | C2 | semidirect |
| 5. C2×#88059 | C2 | semidirect |
| 6. #11718665 | C2 | semidirect |
| 18. C2×#6095 | C4 | semidirect |
| 94. #405 | D13 | semidirect |
| 165. C13 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6095 | 2 |
| C13×#405 | 2 |
| C2×#88064 | 2 |
| C2×#88063 | 2 |
| C2×#88059 | 2 |
| #11718665 | 2 |
| #11718662 | 2 |
| #1977 | 13 |