Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #14271500 | C2 | direct (N × H) |
| 4. C2×#11745155 | C2 | semidirect |
| 5. C2×#11745164 | C2 | semidirect |
| 6. C2×#11745158 | C2 | semidirect |
| 8. C2×C29×#107 | C2 | semidirect |
| 24. C29×#107 | C22 | semidirect |
| 26. #11745164 | C22 | semidirect |
| 27. #11745158 | C22 | semidirect |
| 28. #11745155 | C22 | semidirect |
| 108. C2×#107 | D29 | semidirect |
| 112. C2×C29 | #484 | semidirect |
| 133. #107 | C2×D29 | semidirect |
| 137. C29 | C2×#484 | semidirect |
| 213. C2 | #14271500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745259 | 2 |
| C2×C4⋊C4×D29 | 2 |
| #14271500 | 2 |
| C2×#11745155 | 2 |
| C2×#11745164 | 2 |
| C2×#11745158 | 2 |
| C2×#11745168 | 2 |
| C2×C29×#107 | 2 |
| C2×#484 | 29 |