Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 139 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. C13×#557 | C2 | semidirect |
| 3. #11718746 | C2 | semidirect |
| 4. #11718744 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. C4×#6106 | C2 | semidirect |
| 7. Q8×#1055 | C2 | semidirect |
| 48. Q8×C13 | SD16 | semidirect |
| 61. #1055 | #41 | semidirect |
| 62. #557 | D13 | semidirect |
| 120. C13 | #3392 | semidirect |
| 124. Q8 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| #11719282 | 2 |
| #11718746 | 2 |
| #11718744 | 2 |
| #11718688 | 2 |
| C4×#6106 | 2 |
| Q8×#1055 | 2 |
| #3392 | 13 |