Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C4⋊C4×Dic29 | C2 | semidirect |
| 4. C4×#90781 | C2 | semidirect |
| 5. #14271010 | C2 | semidirect |
| 6. #14271009 | C2 | semidirect |
| 7. #95×D29 | C2 | semidirect |
| 8. C4×C4⋊C4×C29 | C2 | semidirect |
| 20. #11745255 | C4 | semidirect |
| 21. C4×D116 | C4 | semidirect |
| 40. C2×C4×D29 | C2×C4 | semidirect |
| 41. C2×C4×D29 | C2×C4 | semidirect |
| 42. C4⋊C4×C29 | C2×C4 | semidirect |
| 44. C42×C29 | C2×C4 | semidirect |
| 45. #90781 | C2×C4 | semidirect |
| 46. #90781 | C2×C4 | semidirect |
| 47. C4⋊Dic29 | C2×C4 | semidirect |
| 49. C4×Dic29 | C2×C4 | semidirect |
| 74. D116 | C42 | semidirect |
| 98. C4×C4⋊C4 | D29 | semidirect |
| 127. C29 | #2275 | semidirect |
| 144. C4⋊C4 | C4×D29 | semidirect |
| 150. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C2×#11745255 | 2 |
| C4⋊C4×Dic29 | 2 |
| C4×#90781 | 2 |
| #14271010 | 2 |
| #14271009 | 2 |
| #95×D29 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #2275 | 29 |