Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745304 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. #14271713 | C2 | semidirect |
| 4. #14271558 | C2 | semidirect |
| 5. #14271553 | C2 | semidirect |
| 6. #14271545 | C2 | semidirect |
| 7. C4×#90777 | C2 | semidirect |
| 8. C2×C29×#124 | C2 | semidirect |
| 17. C2×#90785 | C22 | semidirect |
| 19. C2×#90784 | C22 | semidirect |
| 25. #11745237 | C22 | semidirect |
| 26. #11745236 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. #11745151 | C22 | semidirect |
| 30. C4×#6597 | C22 | semidirect |
| 59. #90777 | D4 | semidirect |
| 105. C2×#124 | D29 | semidirect |
| 137. C29 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C2×#11745294 | 2 |
| #14271713 | 2 |
| #14271558 | 2 |
| #14271553 | 2 |
| #14271545 | 2 |
| C4×#90777 | 2 |
| C2×C29×#124 | 2 |
| #3153 | 29 |