Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic52 | C2 | semidirect |
| 3. C2×C13×M32 | C2 | semidirect |
| 4. #11718570 | C2 | direct (N × H) |
| 5. C2×Dic104 | C2 | semidirect |
| 6. C2×#88040 | C2 | semidirect |
| 14. C2×Dic52 | C22 | semidirect |
| 19. C13×M32 | C22 | semidirect |
| 21. Dic104 | C22 | semidirect |
| 22. #88040 | C22 | semidirect |
| 75. C2×M32 | D13 | semidirect |
| 100. M32 | C2×D13 | semidirect |
| 103. C2×C13 | #510 | semidirect |
| 131. C13 | C2×#510 | semidirect |
| 165. C2 | #11718570 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic52 | 2 |
| C2×#88158 | 2 |
| C2×C13×M32 | 2 |
| #11718570 | 2 |
| C2×Dic104 | 2 |
| C2×#88040 | 2 |
| C2×#510 | 13 |