Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88200 | C2 | semidirect |
| 2. C22×#6106 | C2 | semidirect |
| 3. C22×#6094 | C2 | semidirect |
| 5. C2×C13×#103 | C2 | semidirect |
| 6. C2×#88061 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718473 | C2 | direct (N × H) |
| 16. #88200 | C22 | semidirect |
| 18. C2×#6106 | C22 | semidirect |
| 25. C2×#6094 | C22 | semidirect |
| 28. C13×#103 | C22 | semidirect |
| 29. #88061 | C22 | semidirect |
| 30. #88047 | C22 | semidirect |
| 62. C2×#1055 | D4 | semidirect |
| 98. #1055 | C2×D4 | semidirect |
| 105. C2×#103 | D13 | semidirect |
| 146. #103 | C2×D13 | semidirect |
| 148. C2×C13 | #468 | semidirect |
| 188. C13 | C2×#468 | semidirect |
| 243. C2 | #11718473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88200 | 2 |
| C22×#6106 | 2 |
| C22×#6094 | 2 |
| C2×#88149 | 2 |
| C2×C13×#103 | 2 |
| C2×#88061 | 2 |
| C2×#88047 | 2 |
| #11718473 | 2 |
| C2×#468 | 13 |