Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 520 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×#11745312 | C2 | semidirect |
| 2. C23×#6597 | C2 | semidirect |
| 3. #14271674 | C2 | semidirect |
| 4. #14271402 | C2 | semidirect |
| 5. #14271397 | C2 | semidirect |
| 6. #14271394 | C2 | semidirect |
| 7. #14271390 | C2 | semidirect |
| 8. #14271199 | C2 | semidirect |
| 9. #14271159 | C2 | semidirect |
| 10. #14271157 | C2 | semidirect |
| 11. C29×#525 | C2 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 24. C2×#90784 | C22 | semidirect |
| 25. C2×#90783 | C22 | semidirect |
| 26. C2×#90782 | C22 | semidirect |
| 37. #11745183 | C22 | semidirect |
| 38. #11745180 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 83. C2×#6597 | D4 | semidirect |
| 131. C22×C29 | #135 | semidirect |
| 146. #525 | D29 | semidirect |
| 191. C29 | #3050 | semidirect |
| 281. C22 | #11745312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| C23×#6597 | 2 |
| #14271674 | 2 |
| #14271402 | 2 |
| #14271397 | 2 |
| #14271394 | 2 |
| #14271390 | 2 |
| #14271199 | 2 |
| #14271159 | 2 |
| #14271157 | 2 |
| C29×#525 | 2 |
| #3050 | 29 |