Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
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. C22×#90784 | C2 | semidirect |
| 3. #14271313 | C2 | direct (N × H) |
| 4. C2×#11745157 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 6. C2×C29×C22⋊Q8 | C2 | semidirect |
| 8. C22×Q8×C29 | C22 | semidirect |
| 16. C29×C22⋊Q8 | C22 | semidirect |
| 18. C2×C4⋊C4×C29 | C22 | semidirect |
| 21. C2×#90784 | C22 | semidirect |
| 22. C22×#6597 | C22 | semidirect |
| 23. C22⋊#6597 | C22 | semidirect |
| 24. #11745157 | C22 | semidirect |
| 33. C2×Q8×C29 | C23 | semidirect |
| 51. C4⋊C4×C29 | C23 | semidirect |
| 55. C2×#6597 | C23 | semidirect |
| 58. C23×C29 | SD16 | semidirect |
| 93. C22×C29 | C2×SD16 | semidirect |
| 108. C2×C22⋊Q8 | D29 | semidirect |
| 113. C2×C29 | #450 | semidirect |
| 119. C22×Q8 | C2×D29 | semidirect |
| 130. C22⋊Q8 | C2×D29 | semidirect |
| 132. C2×C4⋊C4 | C2×D29 | semidirect |
| 136. C29 | C2×#450 | semidirect |
| 145. C2×Q8 | C22×D29 | semidirect |
| 166. C4⋊C4 | C22×D29 | semidirect |
| 178. C23 | #90784 | semidirect |
| 209. C22 | C2×#90784 | semidirect |
| 219. C2 | #14271313 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C22×#90784 | 2 |
| #14271313 | 2 |
| C2×#11745157 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C2×#450 | 29 |