Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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. C2×#11745241 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic29 | C2 | semidirect |
| 3. C22×#90779 | C2 | semidirect |
| 4. C22×#90779 | C2 | semidirect |
| 7. C22×C4×Dic29 | C2 | semidirect |
| 19. C2×C4⋊Dic29 | C22 | semidirect |
| 20. C2×#90779 | C22 | semidirect |
| 21. C2×#90779 | C22 | semidirect |
| 22. C2×C4×Dic29 | C22 | semidirect |
| 23. #11745241 | C22 | direct (N × H) |
| 44. C4⋊Dic29 | C23 | semidirect |
| 45. #90779 | C23 | semidirect |
| 46. #90779 | C23 | semidirect |
| 47. C4×Dic29 | C23 | semidirect |
| 74. C22×C29 | #126 | semidirect |
| 94. C2×C29 | C2×#126 | semidirect |
| 113. C29 | C22×#126 | semidirect |
| 163. C22 | #11745241 | direct (N × H) |
| 175. C2 | C2×#11745241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745241 | 2 |
| C22×C4⋊Dic29 | 2 |
| C22×#90779 | 2 |
| C22×C22⋊Dic29 | 2 |
| C22×C4×Dic29 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C22×#126 | 29 |