Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #14272112 | C2 | semidirect |
| 3. #14272108 | C2 | semidirect |
| 4. C4⋊C4×#1181 | C2 | semidirect |
| 6. C42×#1181 | C2 | semidirect |
| 14. C29×#126 | C4 | semidirect |
| 15. #11745260 | C4 | semidirect |
| 18. #11745241 | C4 | semidirect |
| 19. #11745238 | C4 | semidirect |
| 38. C4⋊C4×C29 | C2×C4 | semidirect |
| 40. C42×C29 | C2×C4 | semidirect |
| 44. C4⋊Dic29 | C2×C4 | semidirect |
| 45. #90779 | C2×C4 | semidirect |
| 46. #90779 | C2×C4 | semidirect |
| 47. C4×Dic29 | C2×C4 | semidirect |
| 81. #1181 | #126 | direct (N × H) |
| 102. #126 | #1181 | direct (N × H) |
| 115. C29 | C4×#126 | semidirect |
| 128. C4⋊C4 | C2×#1181 | semidirect |
| 138. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272113 | 2 |
| #14272112 | 2 |
| #14272108 | 2 |
| C4⋊C4×#1181 | 2 |
| C22⋊C4×#1181 | 2 |
| C42×#1181 | 2 |
| #126×D29 | 2 |
| C4×#126 | 29 |