Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
888 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 354 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 |
|---|---|---|
| 3. #11719059 | C2 | direct (N × H) |
| 8. C2×C42×C13 | C4 | semidirect |
| 9. C2×C4×Dic13 | C4 | semidirect |
| 10. C42×D13 | C4 | semidirect |
| 22. C42×C13 | C2×C4 | semidirect |
| 23. C4×Dic13 | C2×C4 | semidirect |
| 32. C2×C4×C13 | C4⋊C4 | semidirect |
| 34. C2×Dic13 | C4⋊C4 | semidirect |
| 36. C4×D13 | C4⋊C4 | semidirect |
| 50. C4×C13 | C2×C4⋊C4 | semidirect |
| 51. Dic13 | C2×C4⋊C4 | semidirect |
| 59. C2×C42 | #261 | semidirect |
| 60. C2×C13 | #384 | semidirect |
| 62. D13 | #384 | semidirect |
| 76. C42 | C2×#261 | semidirect |
| 77. C13 | C2×#384 | semidirect |
| 90. C2×C4 | C4⋊#261 | semidirect |
| 101. C4 | C2×C4⋊#261 | semidirect |
| 105. C2 | #11719059 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#261 | 2 |
| C2×C42×D13 | 2 |
| #11719059 | 2 |
| C2×#384 | 13 |