Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 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×#88194 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C22×D104 | C2 | semidirect |
| 4. C2×#88147 | C2 | semidirect |
| 5. C2×C13×#102 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 7. C2×#88049 | C2 | semidirect |
| 8. #11718447 | C2 | direct (N × H) |
| 18. #88194 | C22 | semidirect |
| 20. C2×#6104 | C22 | semidirect |
| 25. C2×D104 | C22 | semidirect |
| 27. #88147 | C22 | semidirect |
| 28. C13×#102 | C22 | semidirect |
| 29. #88054 | C22 | semidirect |
| 30. #88049 | C22 | semidirect |
| 51. C2×D52 | D4 | semidirect |
| 93. C2×Dic13 | D8 | semidirect |
| 101. D52 | C2×D4 | semidirect |
| 112. C2×#102 | D13 | semidirect |
| 134. Dic13 | C2×D8 | semidirect |
| 156. #102 | C2×D13 | semidirect |
| 158. C2×C13 | #459 | semidirect |
| 200. C13 | C2×#459 | semidirect |
| 263. C2 | #11718447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88194 | 2 |
| C22×#6104 | 2 |
| C22×D104 | 2 |
| C2×#88147 | 2 |
| C2×C13×#102 | 2 |
| C2×#88054 | 2 |
| C2×#88049 | 2 |
| #11718447 | 2 |
| C2×#459 | 13 |