Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
708 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 197 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×#88140 | C2 | semidirect |
| 4. C4×C13×C22⋊C4 | C2 | semidirect |
| 5. #11718600 | C2 | semidirect |
| 6. #11718596 | C2 | semidirect |
| 7. #11718338 | C2 | semidirect |
| 39. C13×C22⋊C4 | D4 | semidirect |
| 78. C4×C22⋊C4 | D13 | semidirect |
| 93. C4×C13 | #123 | semidirect |
| 139. C22⋊C4 | D52 | semidirect |
| 141. C13 | #2501 | semidirect |
| 182. C4 | #88140 | 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×#88140 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718600 | 2 |
| #11718596 | 2 |
| #11718338 | 2 |
| #2501 | 13 |