Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. C13×#382 | C2 | semidirect |
| 3. #11718627 | C2 | semidirect |
| 4. C2×#88045 | C2 | semidirect |
| 5. #11718122 | C2 | semidirect |
| 34. C42×C13 | D4 | semidirect |
| 68. #382 | D13 | semidirect |
| 123. C42 | D52 | semidirect |
| 124. C13 | #2040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719215 | 2 |
| C13×#382 | 2 |
| #11718627 | 2 |
| C2×#88045 | 2 |
| #11718122 | 2 |
| #2040 | 13 |