Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719437 | C2 | semidirect |
| 3. C13×#498 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718748 | C2 | semidirect |
| 6. #11718528 | C2 | semidirect |
| 7. #11718527 | C2 | semidirect |
| 8. #11718525 | C2 | semidirect |
| 9. #11718521 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 101. #498 | D13 | semidirect |
| 193. C13 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719439 | 2 |
| #11719437 | 2 |
| C13×#498 | 2 |
| #11718752 | 2 |
| #11718748 | 2 |
| #11718528 | 2 |
| #11718527 | 2 |
| #11718525 | 2 |
| #11718521 | 2 |
| C4×#6095 | 2 |
| C8×D52 | 2 |
| #3340 | 13 |