Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 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 |
|---|---|---|
| 1. C23×D116 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. #14271296 | C2 | direct (N × H) |
| 4. C2×#11745157 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 6. C2×C29×#121 | C2 | semidirect |
| 9. C22×D4×C29 | C22 | semidirect |
| 15. C22×D116 | C22 | semidirect |
| 17. C29×#121 | C22 | semidirect |
| 18. C2×C4⋊C4×C29 | C22 | semidirect |
| 21. C2×#90782 | C22 | semidirect |
| 22. C22×#6597 | C22 | semidirect |
| 23. C22⋊#6597 | C22 | semidirect |
| 24. #11745157 | C22 | semidirect |
| 36. C2×D4×C29 | C23 | semidirect |
| 49. C2×D116 | D4 | semidirect |
| 52. C4⋊C4×C29 | C23 | semidirect |
| 56. C2×#6597 | C23 | semidirect |
| 63. C23×C29 | D8 | semidirect |
| 89. D116 | C2×D4 | semidirect |
| 101. C22×C29 | C2×D8 | semidirect |
| 115. C2×#121 | D29 | semidirect |
| 121. C2×C29 | #447 | semidirect |
| 133. C22×D4 | C2×D29 | semidirect |
| 139. #121 | C2×D29 | semidirect |
| 140. C2×C4⋊C4 | C2×D29 | semidirect |
| 144. C29 | C2×#447 | semidirect |
| 164. C2×D4 | C22×D29 | semidirect |
| 175. C4⋊C4 | C22×D29 | semidirect |
| 191. C23 | #90782 | semidirect |
| 224. C22 | C2×#90782 | semidirect |
| 235. C2 | #14271296 | 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×#90782 | 2 |
| #14271296 | 2 |
| C2×#11745157 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×#121 | 2 |
| C2×#447 | 29 |