Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#500 | C2 | semidirect |
| 3. #11718754 | C2 | semidirect |
| 5. #11718534 | C2 | semidirect |
| 6. #11718360 | C2 | semidirect |
| 58. C4×D13 | Q16 | semidirect |
| 63. #500 | D13 | semidirect |
| 122. C13 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| C13×#500 | 2 |
| #11718754 | 2 |
| #11718548 | 2 |
| #11718534 | 2 |
| #11718360 | 2 |
| C4×C8×D13 | 2 |
| #3170 | 13 |