Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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. C23×Dic26 | C2 | semidirect |
| 4. C2×C13×#95 | C2 | semidirect |
| 5. C2×#88071 | C2 | semidirect |
| 6. #11718334 | C2 | direct (N × H) |
| 14. C22×Dic26 | C22 | semidirect |
| 19. C13×#95 | C22 | semidirect |
| 20. #88071 | C22 | semidirect |
| 26. C23×D13 | Q8 | semidirect |
| 63. C22×D13 | C2×Q8 | semidirect |
| 84. C2×#95 | D13 | semidirect |
| 118. #95 | C2×D13 | semidirect |
| 119. C2×C13 | #393 | semidirect |
| 152. C13 | C2×#393 | semidirect |
| 205. C2 | #11718334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic26 | 2 |
| C22×#6103 | 2 |
| C2×C13×#95 | 2 |
| C2×#88071 | 2 |
| #11718334 | 2 |
| C2×#393 | 13 |