Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
680 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 469 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. C2×#11745163 | C2 | direct (N × H) |
| 7. C22×C8×C29 | C4 | semidirect |
| 11. C22×#6597 | C4 | semidirect |
| 13. #11745163 | C22 | direct (N × H) |
| 21. C2×C8×C29 | C2×C4 | semidirect |
| 25. C2×#6597 | C2×C4 | semidirect |
| 37. C8×C29 | C22×C4 | semidirect |
| 38. #6597 | C22×C4 | semidirect |
| 40. C22×C29 | #97 | semidirect |
| 52. C2×C29 | C2×#97 | semidirect |
| 59. C22×C8 | Dic29 | semidirect |
| 64. C29 | C22×#97 | semidirect |
| 74. C2×C8 | C2×Dic29 | semidirect |
| 89. C8 | C22×Dic29 | semidirect |
| 90. C22 | #11745163 | direct (N × H) |
| 98. C2 | C2×#11745163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6597 | 2 |
| C22×C4×Dic29 | 2 |
| C2×#11745163 | 2 |
| C23×C8×C29 | 2 |
| C22×#97 | 29 |