Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719435 | C2 | semidirect |
| 3. C13×#498 | C2 | semidirect |
| 4. #11718755 | C2 | semidirect |
| 5. #11718745 | C2 | semidirect |
| 6. #11718525 | C2 | semidirect |
| 7. #11718524 | C2 | semidirect |
| 8. #11718523 | C2 | semidirect |
| 9. D13×#106 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 91. D52 | SD16 | semidirect |
| 100. C8×C13 | #41 | semidirect |
| 104. #498 | D13 | semidirect |
| 197. C13 | #3335 | semidirect |
| 224. C8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| #11719431 | 2 |
| C13×#498 | 2 |
| #11718755 | 2 |
| #11718745 | 2 |
| #11718525 | 2 |
| #11718524 | 2 |
| #11718523 | 2 |
| D13×#106 | 2 |
| C4×#6095 | 2 |
| C8×D52 | 2 |
| #3335 | 13 |