Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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×#88147 | C2 | semidirect |
| 3. C13×#384 | C2 | semidirect |
| 4. #11718649 | C2 | semidirect |
| 5. C42×Dic13 | C2 | semidirect |
| 14. #88128 | C4 | semidirect |
| 22. C2×D52 | C2×C4 | semidirect |
| 25. C42×C13 | C2×C4 | semidirect |
| 28. C4×Dic13 | D4 | semidirect |
| 46. #384 | D13 | semidirect |
| 55. C4×C13 | C4×D4 | semidirect |
| 57. Dic13 | #127 | semidirect |
| 84. C42 | C4×D13 | semidirect |
| 85. C13 | C4×#127 | semidirect |
| 108. C4 | #88147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88147 | 2 |
| C2×#88128 | 2 |
| C13×#384 | 2 |
| #11718649 | 2 |
| C42×Dic13 | 2 |
| C4×#127 | 13 |