Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
432 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 244 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. Q8×#1057 | C2 | semidirect |
| 3. D4×#1057 | C2 | semidirect |
| 4. #11719119 | C2 | semidirect |
| 5. C2×C4⋊#1057 | C2 | semidirect |
| 19. C13×#41 | C8 | semidirect |
| 37. Q8×C13 | C2×C8 | semidirect |
| 38. D4×C13 | C2×C8 | semidirect |
| 39. C2×C4×C13 | C2×C8 | semidirect |
| 84. #41 | #1057 | semidirect |
| 100. C13 | #2988 | semidirect |
| 102. Q8 | C2×#1057 | semidirect |
| 103. D4 | C2×#1057 | semidirect |
| 111. C2×C4 | C2×#1057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic13 | 2 |
| Q8×#1057 | 2 |
| D4×#1057 | 2 |
| #11719119 | 2 |
| C2×C4⋊#1057 | 2 |
| #2988 | 13 |