Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×C13×M16 | C2 | semidirect |
| 2. #11719496 | C2 | semidirect |
| 3. C2×#88158 | C2 | semidirect |
| 4. #11718798 | C2 | semidirect |
| 5. #11718796 | C2 | semidirect |
| 6. #11718795 | C2 | semidirect |
| 7. #11718774 | C2 | semidirect |
| 8. #11718767 | C2 | semidirect |
| 22. C2×Dic52 | C22 | semidirect |
| 24. C2×D104 | C22 | semidirect |
| 25. C2×#6095 | C22 | semidirect |
| 26. #88061 | C22 | semidirect |
| 27. #88058 | C22 | semidirect |
| 28. #88057 | C22 | semidirect |
| 29. #88056 | C22 | semidirect |
| 47. C2×C8×C13 | D4 | semidirect |
| 88. C22×M16 | D13 | semidirect |
| 155. C2×C8 | C22⋊D13 | semidirect |
| 165. C13 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×M16 | 2 |
| #11719496 | 2 |
| C2×#88158 | 2 |
| #11718798 | 2 |
| #11718796 | 2 |
| #11718795 | 2 |
| #11718774 | 2 |
| #11718767 | 2 |
| #3054 | 13 |