Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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×#555 | C2 | semidirect |
| 2. #11719260 | C2 | semidirect |
| 3. #11718745 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. #11718700 | C2 | semidirect |
| 6. #11718695 | C2 | semidirect |
| 7. C4×#6104 | C2 | semidirect |
| 8. #11718673 | C2 | semidirect |
| 9. #11718668 | C2 | semidirect |
| 10. #11718664 | C2 | semidirect |
| 11. #11718656 | C2 | semidirect |
| 102. #1055 | #41 | semidirect |
| 103. #555 | D13 | semidirect |
| 201. C13 | #3354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#555 | 2 |
| #11719260 | 2 |
| #11718745 | 2 |
| #11718740 | 2 |
| #11718700 | 2 |
| #11718695 | 2 |
| C4×#6104 | 2 |
| #11718673 | 2 |
| #11718668 | 2 |
| #11718664 | 2 |
| #11718656 | 2 |
| #3354 | 13 |