Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271697 | C2 | semidirect |
| 2. #14271493 | C2 | semidirect |
| 3. #14271476 | C2 | semidirect |
| 4. #14271463 | C2 | semidirect |
| 5. #14271378 | C2 | semidirect |
| 6. #14271314 | C2 | semidirect |
| 8. #14271273 | C2 | semidirect |
| 9. #14271263 | C2 | semidirect |
| 10. #14271220 | C2 | semidirect |
| 11. C2×C4×D4×C29 | C2 | semidirect |
| 28. #11745237 | C22 | semidirect |
| 29. C4×D116 | C22 | semidirect |
| 31. #11745232 | C22 | semidirect |
| 32. C4×Dic58 | C22 | semidirect |
| 37. #11745158 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 41. C4⋊#6597 | C22 | semidirect |
| 42. #11745151 | C22 | semidirect |
| 136. C2×C4×D4 | D29 | semidirect |
| 183. C29 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271697 | 2 |
| #14271493 | 2 |
| #14271476 | 2 |
| #14271463 | 2 |
| #14271378 | 2 |
| #14271314 | 2 |
| #14271297 | 2 |
| #14271273 | 2 |
| #14271263 | 2 |
| #14271220 | 2 |
| C2×C4×D4×C29 | 2 |
| #3114 | 29 |