Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×#88240 | C2 | semidirect |
| 3. #11719159 | C2 | semidirect |
| 4. #11719076 | C2 | semidirect |
| 5. #11719073 | C2 | semidirect |
| 6. #11719052 | C2 | semidirect |
| 7. C4×D13⋊C8 | C2 | semidirect |
| 42. D13⋊C8 | D4 | semidirect |
| 83. C4×C13 | #131 | semidirect |
| 131. C13 | #2931 | semidirect |
| 162. C4 | #88240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88240 | 2 |
| #11719430 | 2 |
| #11719159 | 2 |
| #11719076 | 2 |
| #11719073 | 2 |
| #11719052 | 2 |
| C4×D13⋊C8 | 2 |
| #2931 | 13 |