Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
406 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 160 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. #14272213 | C2 | semidirect |
| 2. #14272195 | C2 | semidirect |
| 3. #14272191 | C2 | semidirect |
| 4. #14272185 | C2 | semidirect |
| 5. #14272184 | C2 | semidirect |
| 6. C4×#90800 | C2 | semidirect |
| 7. #14272122 | C2 | semidirect |
| 75. D116 | M16 | semidirect |
| 82. #6599 | #41 | semidirect |
| 135. C29 | #2970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272213 | 2 |
| #14272195 | 2 |
| #14272191 | 2 |
| #14272185 | 2 |
| #14272184 | 2 |
| C4×#90800 | 2 |
| #14272122 | 2 |
| #14271631 | 2 |
| #2970 | 29 |