Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
740 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#261 | C2 | semidirect |
| 3. #11719151 | C2 | semidirect |
| 4. #11719150 | C2 | semidirect |
| 5. #11719060 | C2 | semidirect |
| 6. #11719057 | C2 | semidirect |
| 16. C13×#127 | C4 | semidirect |
| 17. #88194 | C4 | semidirect |
| 18. #88194 | C4 | semidirect |
| 19. #88128 | C4 | semidirect |
| 29. C2×D4×C13 | C2×C4 | semidirect |
| 30. C2×D4×C13 | C2×C4 | semidirect |
| 31. C2×C22⋊D13 | C2×C4 | semidirect |
| 32. C2×C22⋊D13 | C2×C4 | semidirect |
| 36. C2×D52 | C2×C4 | semidirect |
| 37. C2×D52 | C2×C4 | semidirect |
| 44. C4×#261 | D4 | semidirect |
| 45. C42×C13 | C2×C4 | semidirect |
| 46. C4×Dic13 | C2×C4 | semidirect |
| 47. C4×Dic13 | C2×C4 | semidirect |
| 106. #127 | #261 | semidirect |
| 130. C2×D4 | C2×#261 | semidirect |
| 131. C2×D4 | C2×#261 | semidirect |
| 146. C42 | C2×#261 | semidirect |
| 147. C13 | #2328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#261 | 2 |
| D13×#127 | 2 |
| #11719151 | 2 |
| #11719150 | 2 |
| #11719060 | 2 |
| #11719057 | 2 |
| #2328 | 13 |