Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745294 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. #14271378 | C2 | semidirect |
| 4. #14271368 | C2 | semidirect |
| 5. #14271358 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271162 | C2 | semidirect |
| 8. C2×C4×D4×C29 | C2 | semidirect |
| 25. #11745237 | C22 | semidirect |
| 26. #11745236 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 31. #11745157 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 33. C4⋊#6597 | C22 | semidirect |
| 37. C2×D4×C29 | D4 | semidirect |
| 120. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 126. C2×C4×D4 | D29 | semidirect |
| 163. C29 | #3036 | semidirect |
| 174. C2×D4 | D116 | semidirect |
| 250. C4 | #11745294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271713 | 2 |
| #14271378 | 2 |
| #14271368 | 2 |
| #14271358 | 2 |
| #14271187 | 2 |
| #14271162 | 2 |
| C2×C4×D4×C29 | 2 |
| #3036 | 29 |