Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#88074 | C2 | semidirect |
| 3. C2×#88073 | C2 | semidirect |
| 4. #11718131 | C2 | semidirect |
| 5. #11718128 | C2 | semidirect |
| 6. C22×D4×C13 | C4 | semidirect |
| 9. C13×#123 | C4 | semidirect |
| 14. C13×#120 | C4 | semidirect |
| 16. C2×C13×C22⋊C4 | C4 | semidirect |
| 24. C24×C13 | C2×C4 | semidirect |
| 39. C22×C4×C13 | C2×C4 | semidirect |
| 49. C13×C22⋊C4 | C2×C4 | semidirect |
| 50. C13×C22⋊C4 | C2×C4 | semidirect |
| 123. C22×D4 | Dic13 | semidirect |
| 127. #123 | Dic13 | semidirect |
| 132. #120 | Dic13 | semidirect |
| 135. C2×C22⋊C4 | Dic13 | semidirect |
| 150. C24 | C2×Dic13 | semidirect |
| 166. C22×C4 | C2×Dic13 | semidirect |
| 180. C22⋊C4 | C2×Dic13 | semidirect |
| 181. C22⋊C4 | C2×Dic13 | semidirect |
| 182. C13 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#534 | 2 |
| C2×#88074 | 2 |
| C2×#88073 | 2 |
| #11718131 | 2 |
| #11718128 | 2 |
| #2121 | 13 |