Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×C13×M32 | C2 | semidirect |
| 3. C22×#6090 | C2 | semidirect |
| 4. #11718568 | C2 | direct (N × H) |
| 5. C2×#88038 | C2 | semidirect |
| 6. C2×C16×D13 | C2 | semidirect |
| 14. C13×M32 | C22 | semidirect |
| 18. C2×#6090 | C22 | semidirect |
| 19. #88038 | C22 | semidirect |
| 20. C16×D13 | C22 | semidirect |
| 60. C2×M32 | D13 | semidirect |
| 80. M32 | C2×D13 | semidirect |
| 87. C2×C13 | #504 | semidirect |
| 109. C13 | C2×#504 | semidirect |
| 137. C2 | #11718568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88155 | 2 |
| C2×C13×M32 | 2 |
| C22×#6090 | 2 |
| #11718568 | 2 |
| C2×#88038 | 2 |
| C2×C16×D13 | 2 |
| C2×#504 | 13 |