Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
452 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 156 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. #11719145 | C2 | semidirect |
| 3. #11719127 | C2 | semidirect |
| 4. #11719126 | C2 | semidirect |
| 5. #11719076 | C2 | semidirect |
| 6. #11719066 | C2 | semidirect |
| 7. #11719051 | C2 | semidirect |
| 8. #11719049 | C2 | semidirect |
| 11. C2×#6122 | C22 | semidirect |
| 12. C2×#6118 | C22 | semidirect |
| 22. C22⋊#1057 | C22 | semidirect |
| 23. #88112 | C22 | semidirect |
| 27. #88111 | C22 | semidirect |
| 28. C4⋊#1057 | C22 | semidirect |
| 29. C4×#1057 | C22 | semidirect |
| 30. C4×#1057 | C22 | semidirect |
| 86. C4×D13 | M16 | semidirect |
| 175. C13 | #2975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D13 | 2 |
| #11719145 | 2 |
| #11719127 | 2 |
| #11719126 | 2 |
| #11719076 | 2 |
| #11719066 | 2 |
| #11719051 | 2 |
| #11719049 | 2 |
| #2975 | 13 |