Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #11719268 | C2 | semidirect |
| 2. #11719260 | C2 | semidirect |
| 3. C4×C13×D8 | C2 | semidirect |
| 4. #11718819 | C2 | semidirect |
| 5. #11718680 | C2 | semidirect |
| 6. #11718669 | C2 | semidirect |
| 7. #11718549 | C2 | semidirect |
| 8. #11718439 | C2 | semidirect |
| 9. #11718433 | C2 | semidirect |
| 10. C8×D52 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 114. C4×D8 | D13 | semidirect |
| 206. C13 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719268 | 2 |
| #11719260 | 2 |
| C4×C13×D8 | 2 |
| #11718819 | 2 |
| #11718680 | 2 |
| #11718669 | 2 |
| #11718549 | 2 |
| #11718439 | 2 |
| #11718433 | 2 |
| C8×D52 | 2 |
| #11718342 | 2 |
| #3303 | 13 |