Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#88257 | C2 | semidirect |
| 2. C2×C13×#131 | C2 | semidirect |
| 3. #11719458 | C2 | direct (N × H) |
| 4. C2×#88163 | C2 | semidirect |
| 5. C22×Dic52 | C2 | semidirect |
| 6. C2×#88158 | C2 | semidirect |
| 9. #88257 | C22 | semidirect |
| 14. C13×#131 | C22 | semidirect |
| 17. #88163 | C22 | semidirect |
| 20. C2×Dic52 | C22 | semidirect |
| 21. #88158 | C22 | semidirect |
| 74. C2×#131 | D13 | semidirect |
| 98. #131 | C2×D13 | semidirect |
| 102. C2×C13 | #578 | semidirect |
| 130. C13 | C2×#578 | semidirect |
| 161. C2 | #11719458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88257 | 2 |
| C2×C13×#131 | 2 |
| #11719458 | 2 |
| C2×#88163 | 2 |
| C22×Dic52 | 2 |
| C2×#88158 | 2 |
| C2×#578 | 13 |