Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic13 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 6. #11718825 | C2 | direct (N × H) |
| 7. C2×#88058 | C2 | semidirect |
| 8. C2×#88055 | C2 | semidirect |
| 12. C2×C13×SD16 | C4 | semidirect |
| 17. Q8×Dic13 | C22 | semidirect |
| 26. #88075 | C22 | semidirect |
| 28. #88058 | C22 | semidirect |
| 29. #88055 | C22 | semidirect |
| 33. C2×Q8×C13 | C2×C4 | semidirect |
| 47. C13×SD16 | C2×C4 | semidirect |
| 48. C2×C8×C13 | C2×C4 | semidirect |
| 69. Q8×C13 | C22×C4 | semidirect |
| 88. C8×C13 | C22×C4 | semidirect |
| 117. C2×SD16 | Dic13 | semidirect |
| 136. C2×C13 | #440 | semidirect |
| 143. C2×Q8 | C2×Dic13 | semidirect |
| 157. SD16 | C2×Dic13 | semidirect |
| 160. C2×C8 | C2×Dic13 | semidirect |
| 171. C13 | C2×#440 | semidirect |
| 179. Q8 | C22×Dic13 | semidirect |
| 199. C8 | C22×Dic13 | semidirect |
| 217. C2 | #11718825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| C2×Q8×Dic13 | 2 |
| C2×D4×Dic13 | 2 |
| C2×#88075 | 2 |
| C2×#88072 | 2 |
| #11718825 | 2 |
| C2×#88058 | 2 |
| C2×#88055 | 2 |
| C2×#440 | 13 |