Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #11719289 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. C13×#446 | C2 | semidirect |
| 4. #11718511 | C2 | semidirect |
| 5. #11718507 | C2 | semidirect |
| 7. #11718502 | C2 | semidirect |
| 8. #11718375 | C2 | semidirect |
| 9. #11718371 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 109. #446 | D13 | semidirect |
| 196. C13 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719289 | 2 |
| Q8×D52 | 2 |
| C13×#446 | 2 |
| #11718511 | 2 |
| #11718507 | 2 |
| #11718505 | 2 |
| #11718502 | 2 |
| #11718375 | 2 |
| #11718371 | 2 |
| C4×D104 | 2 |
| #11718342 | 2 |
| #3367 | 13 |