Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#90784 | C2 | semidirect |
| 2. C2×#11745310 | C2 | semidirect |
| 4. #14271411 | C2 | semidirect |
| 5. #14271394 | C2 | semidirect |
| 6. #14271199 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#536 | C2 | semidirect |
| 16. C29×C22⋊Q8 | C22 | semidirect |
| 28. C2×#90777 | C22 | semidirect |
| 30. C22×#6597 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 33. #11745156 | C22 | semidirect |
| 34. #11745155 | C22 | semidirect |
| 67. C2×#6597 | D4 | semidirect |
| 118. #536 | D29 | semidirect |
| 146. C22⋊Q8 | C2×D29 | semidirect |
| 155. C29 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745310 | 2 |
| #14271727 | 2 |
| #14271411 | 2 |
| #14271394 | 2 |
| #14271199 | 2 |
| #14271172 | 2 |
| #14271167 | 2 |
| C29×#536 | 2 |
| #3057 | 29 |