Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×C22⋊Q8 | C2 | semidirect |
| 3. C22×#6106 | C2 | semidirect |
| 4. C2×C22⋊#1055 | C2 | semidirect |
| 5. #11718707 | C2 | direct (N × H) |
| 6. C2×#88049 | C2 | semidirect |
| 8. C22×Q8×C13 | C22 | semidirect |
| 16. C13×C22⋊Q8 | C22 | semidirect |
| 18. C2×C13×C4⋊C4 | C22 | semidirect |
| 21. C2×#6106 | C22 | semidirect |
| 22. C22×#1055 | C22 | semidirect |
| 23. C22⋊#1055 | C22 | semidirect |
| 24. #88049 | C22 | semidirect |
| 33. C2×Q8×C13 | C23 | semidirect |
| 51. C13×C4⋊C4 | C23 | semidirect |
| 55. C2×#1055 | C23 | semidirect |
| 59. C23×C13 | SD16 | semidirect |
| 90. C2×C22⋊Q8 | D13 | semidirect |
| 99. C22×C13 | C2×SD16 | semidirect |
| 113. C22×Q8 | C2×D13 | semidirect |
| 124. C22⋊Q8 | C2×D13 | semidirect |
| 126. C2×C4⋊C4 | C2×D13 | semidirect |
| 131. C2×C13 | #450 | semidirect |
| 144. C2×Q8 | C22×D13 | semidirect |
| 165. C4⋊C4 | C22×D13 | semidirect |
| 167. C13 | C2×#450 | semidirect |
| 178. C23 | #6106 | semidirect |
| 209. C22 | C2×#6106 | semidirect |
| 219. C2 | #11718707 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×C13×C22⋊Q8 | 2 |
| C22×#6106 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718707 | 2 |
| C2×#88049 | 2 |
| C2×#450 | 13 |