Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C13×C4⋊C4 | C2 | semidirect |
| 3. C2×C22⋊#1055 | C2 | semidirect |
| 4. #11718629 | C2 | direct (N × H) |
| 5. C2×#88049 | C2 | semidirect |
| 6. C2×#88048 | C2 | semidirect |
| 14. C2×C13×C4⋊C4 | C22 | semidirect |
| 20. C22⋊#1055 | C22 | semidirect |
| 21. #88049 | C22 | semidirect |
| 22. #88048 | C22 | semidirect |
| 74. C22×C4⋊C4 | D13 | semidirect |
| 107. C2×C4⋊C4 | C2×D13 | semidirect |
| 113. C2×C13 | #481 | semidirect |
| 142. C13 | C2×#481 | semidirect |
| 187. C2 | #11718629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C4⋊C4 | 2 |
| C2×#88184 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718629 | 2 |
| C2×#88049 | 2 |
| C2×#88048 | 2 |
| C2×#481 | 13 |