Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
540 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 217 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. #14271070 | C2 | semidirect |
| 2. #14271056 | C2 | semidirect |
| 3. #14271056 | C2 | semidirect |
| 5. #14271038 | C2 | semidirect |
| 6. #14271031 | C2 | semidirect |
| 7. C4×C4⋊Dic29 | C2 | semidirect |
| 8. C22⋊C4×Dic29 | C2 | semidirect |
| 13. C29×#124 | C4 | semidirect |
| 34. C2×Q8×C29 | C2×C4 | semidirect |
| 48. C22⋊C4×C29 | C2×C4 | semidirect |
| 49. C22⋊C4×C29 | C2×C4 | semidirect |
| 50. C42×C29 | C2×C4 | semidirect |
| 131. #124 | Dic29 | semidirect |
| 150. C29 | #2337 | semidirect |
| 153. C2×Q8 | C2×Dic29 | semidirect |
| 172. C22⋊C4 | C2×Dic29 | semidirect |
| 173. C22⋊C4 | C2×Dic29 | semidirect |
| 177. C42 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271070 | 2 |
| #14271056 | 2 |
| #14271043 | 2 |
| #14271038 | 2 |
| #14271031 | 2 |
| C4×C4⋊Dic29 | 2 |
| C22⋊C4×Dic29 | 2 |
| C2×C29×#124 | 2 |
| #2337 | 29 |