Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11719136 | C2 | semidirect |
| 4. #11719070 | C2 | semidirect |
| 11. C2×C4⋊#261 | C22 | semidirect |
| 12. C2×C13×C22⋊C4 | C4 | semidirect |
| 13. C2×C22⋊Dic13 | C4 | semidirect |
| 14. C2×#6103 | C4 | semidirect |
| 15. C22⋊C4×D13 | C4 | semidirect |
| 17. (C2×#261)⋊C4 | C22 | semidirect |
| 29. C22×C4×C13 | C2×C4 | semidirect |
| 30. C22×Dic13 | C2×C4 | semidirect |
| 32. C2×C4×D13 | C2×C4 | semidirect |
| 37. C13×C22⋊C4 | C2×C4 | semidirect |
| 38. C22⋊Dic13 | C2×C4 | semidirect |
| 39. #6103 | C2×C4 | semidirect |
| 42. C23×C13 | C4⋊C4 | semidirect |
| 51. C22×D13 | C4⋊C4 | semidirect |
| 52. C22×D13 | C4⋊C4 | semidirect |
| 106. C2×C22⋊C4 | #261 | semidirect |
| 131. C22×C4 | C2×#261 | semidirect |
| 137. C22⋊C4 | C2×#261 | semidirect |
| 138. C13 | #2315 | semidirect |
| 155. C23 | C4⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#261 | 2 |
| C2×C22⋊C4×D13 | 2 |
| #11719136 | 2 |
| #11719070 | 2 |
| #2315 | 13 |