Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #14271640 | C2 | semidirect |
| 4. #14271262 | C2 | semidirect |
| 5. #14271250 | C2 | semidirect |
| 6. #14271171 | C2 | semidirect |
| 8. #14271118 | C2 | semidirect |
| 9. C29×#427 | C2 | semidirect |
| 17. C2×#90773 | C4 | semidirect |
| 21. #11745249 | C22 | semidirect |
| 26. C29×#107 | C22 | semidirect |
| 27. C29×#106 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 42. C2×Dic58 | C2×C4 | semidirect |
| 44. C2×C8×C29 | C2×C4 | semidirect |
| 61. #90773 | C2×C4 | semidirect |
| 62. #90773 | C2×C4 | semidirect |
| 105. #427 | D29 | semidirect |
| 129. #107 | C2×D29 | semidirect |
| 130. #106 | C2×D29 | semidirect |
| 135. C29 | #2949 | semidirect |
| 152. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| #14271640 | 2 |
| #14271637 | 2 |
| #14271262 | 2 |
| #14271250 | 2 |
| #14271171 | 2 |
| #14271167 | 2 |
| #14271118 | 2 |
| C29×#427 | 2 |
| #2949 | 29 |