Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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 |
| 2. #11719248 | C2 | semidirect |
| 3. C13×#476 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 6. #11718532 | C2 | semidirect |
| 7. #11718519 | C2 | semidirect |
| 8. #11718503 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 10. #11718424 | C2 | semidirect |
| 57. #6104 | Q8 | semidirect |
| 105. #476 | D13 | semidirect |
| 191. C13 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| #11719248 | 2 |
| C13×#476 | 2 |
| #11718739 | 2 |
| C4×#6104 | 2 |
| #11718532 | 2 |
| #11718519 | 2 |
| #11718503 | 2 |
| #11718491 | 2 |
| #11718424 | 2 |
| #11718417 | 2 |
| #3380 | 13 |