Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 2. C22×C22⋊#261 | C2 | semidirect |
| 3. C2×#88107 | C2 | direct (N × H) |
| 4. C24×D13 | C4 | semidirect |
| 7. C23×C4×C13 | C4 | semidirect |
| 10. C22×D52 | C4 | semidirect |
| 13. C2×C22⋊#261 | C22 | semidirect |
| 14. #88107 | C22 | direct (N × H) |
| 21. C23×D13 | C2×C4 | semidirect |
| 29. C22×C4×C13 | C2×C4 | semidirect |
| 34. C2×D52 | C2×C4 | semidirect |
| 37. C22⋊#261 | C23 | semidirect |
| 55. C22×D13 | C22×C4 | semidirect |
| 63. C2×C4×C13 | C22×C4 | semidirect |
| 71. C22×C13 | #99 | semidirect |
| 96. C23×C4 | #261 | semidirect |
| 102. C2×C13 | C2×#99 | semidirect |
| 127. C22×C4 | C2×#261 | semidirect |
| 130. C13 | C22×#99 | semidirect |
| 157. C2×C4 | C22×#261 | semidirect |
| 172. C22 | #88107 | direct (N × H) |
| 183. C2 | C2×#88107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C22×C22⋊#261 | 2 |
| C2×#88107 | 2 |
| C22×#99 | 13 |