Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88198 | C2 | semidirect |
| 5. C2×C13×#103 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 7. C2×#88050 | C2 | semidirect |
| 8. #11718479 | C2 | direct (N × H) |
| 16. #88198 | C22 | semidirect |
| 28. C13×#103 | C22 | semidirect |
| 29. #88054 | C22 | semidirect |
| 30. #88050 | C22 | semidirect |
| 85. C2×Dic13 | SD16 | semidirect |
| 104. C2×#103 | D13 | semidirect |
| 120. Dic13 | C2×SD16 | semidirect |
| 142. #103 | C2×D13 | semidirect |
| 143. C2×C13 | #461 | semidirect |
| 182. C13 | C2×#461 | semidirect |
| 231. C2 | #11718479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88198 | 2 |
| C22×#6106 | 2 |
| C22×#6095 | 2 |
| C2×#88147 | 2 |
| C2×C13×#103 | 2 |
| C2×#88054 | 2 |
| C2×#88050 | 2 |
| #11718479 | 2 |
| C2×#461 | 13 |