Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11719471 | C2 | semidirect |
| 2. C2×C13×Q32 | C2 | semidirect |
| 3. #11718840 | C2 | semidirect |
| 4. #11718580 | C2 | semidirect |
| 5. #11718579 | C2 | semidirect |
| 6. D13×Q32 | C2 | semidirect |
| 7. #11718565 | C2 | semidirect |
| 8. #11718562 | C2 | semidirect |
| 76. C2×Q32 | D13 | semidirect |
| 131. C13 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719471 | 2 |
| C2×C13×Q32 | 2 |
| #11718840 | 2 |
| #11718580 | 2 |
| #11718579 | 2 |
| D13×Q32 | 2 |
| #11718565 | 2 |
| #11718562 | 2 |
| #3417 | 13 |