Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1104 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×#88237 | C2 | semidirect |
| 3. #11719171 | C2 | semidirect |
| 4. #11719151 | C2 | semidirect |
| 6. C22×D4×C13 | C4 | semidirect |
| 7. C22×C22⋊D13 | C4 | semidirect |
| 9. C2×D4×D13 | C4 | semidirect |
| 11. C22×D52 | C4 | semidirect |
| 14. C2×C22⋊#261 | C22 | semidirect |
| 16. C2×C4⋊#261 | C22 | semidirect |
| 17. C2×C4×#261 | C22 | semidirect |
| 64. C2×C4×C13 | C22⋊C4 | semidirect |
| 67. C2×Dic13 | C22⋊C4 | semidirect |
| 70. C4×D13 | C22⋊C4 | semidirect |
| 102. C22×D4 | #261 | semidirect |
| 142. C13 | #2309 | semidirect |
| 169. C2×C4 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C2×#88237 | 2 |
| #11719171 | 2 |
| #11719151 | 2 |
| #2309 | 13 |