Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 121 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×C4⋊Dic13 | C2 | semidirect |
| 3. C2×C13×C22⋊C8 | C2 | semidirect |
| 4. C2×#88061 | C2 | semidirect |
| 5. #11718143 | C2 | semidirect |
| 12. #88184 | C4 | semidirect |
| 39. C2×D52 | C2×C4 | semidirect |
| 47. C4⋊Dic13 | C2×C4 | semidirect |
| 48. C4⋊Dic13 | D4 | semidirect |
| 88. C2×C22⋊C8 | D13 | semidirect |
| 96. C22×C13 | #102 | semidirect |
| 168. C13 | #1874 | semidirect |
| 217. C22 | #88061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C22×C4⋊Dic13 | 2 |
| C2×C13×C22⋊C8 | 2 |
| C2×#88061 | 2 |
| #11718143 | 2 |
| #1874 | 13 |