Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
422 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 148 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. #11719147 | C2 | semidirect |
| 3. #11719146 | C2 | semidirect |
| 4. D13⋊(C22⋊C8) | C2 | semidirect |
| 5. #11719075 | C2 | semidirect |
| 6. #11719073 | C2 | semidirect |
| 7. #11719068 | C2 | semidirect |
| 8. #11719065 | C2 | semidirect |
| 9. #11719063 | C2 | semidirect |
| 12. C2×#6122 | C22 | semidirect |
| 13. C22×#1057 | C22 | semidirect |
| 14. C2×#6118 | C22 | semidirect |
| 17. C2×D13⋊C8 | C22 | semidirect |
| 29. C22⋊#1057 | C22 | semidirect |
| 30. #88112 | C22 | semidirect |
| 33. #88111 | C22 | semidirect |
| 34. #88110 | C22 | semidirect |
| 35. C4⋊#1057 | C22 | semidirect |
| 36. C4×#1057 | C22 | semidirect |
| 206. C13 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719361 | 2 |
| #11719147 | 2 |
| #11719146 | 2 |
| D13⋊(C22⋊C8) | 2 |
| #11719075 | 2 |
| #11719073 | 2 |
| #11719068 | 2 |
| #11719065 | 2 |
| #11719063 | 2 |
| #2977 | 13 |