Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×C13×#135 | C2 | semidirect |
| 2. #11719538 | C2 | semidirect |
| 3. C2×#88155 | C2 | semidirect |
| 4. #11718893 | C2 | semidirect |
| 5. #11718849 | C2 | semidirect |
| 6. #11718835 | C2 | semidirect |
| 7. #11718818 | C2 | semidirect |
| 8. C2×#88058 | C2 | semidirect |
| 48. C2×C8×C13 | D4 | semidirect |
| 87. C2×#135 | D13 | semidirect |
| 160. C2×C8 | C22⋊D13 | semidirect |
| 168. C13 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11719538 | 2 |
| C2×#88155 | 2 |
| #11718893 | 2 |
| #11718849 | 2 |
| #11718835 | 2 |
| #11718818 | 2 |
| C2×#88058 | 2 |
| #3061 | 13 |