Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
180 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 74 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. Q8×#1057 | C2 | semidirect |
| 4. Q8⋊#1057 | C2 | semidirect |
| 6. #11718253 | C2 | semidirect |
| 7. C8×#1057 | C2 | semidirect |
| 32. C13×SD16 | C8 | semidirect |
| 44. Q8×C13 | C2×C8 | semidirect |
| 59. #1057 | SD16 | direct (N × H) |
| 60. C8×C13 | C2×C8 | semidirect |
| 103. SD16 | #1057 | direct (N × H) |
| 118. C13 | C8×SD16 | semidirect |
| 121. Q8 | C2×#1057 | semidirect |
| 138. C8 | C2×#1057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1057 | 2 |
| D4×#1057 | 2 |
| SD16×Dic13 | 2 |
| Q8⋊#1057 | 2 |
| D4⋊#1057 | 2 |
| #11718253 | 2 |
| C8×#1057 | 2 |
| C8×SD16 | 13 |