Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#11745183 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. C2×#11745157 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. #14271020 | C2 | semidirect |
| 7. C2×C29×#103 | C2 | semidirect |
| 14. C2×#90809 | C4 | semidirect |
| 94. Q8×C29 | C22⋊C4 | semidirect |
| 117. D116 | C22⋊C4 | semidirect |
| 157. C2×#103 | D29 | semidirect |
| 193. C29 | #1788 | semidirect |
| 258. Q8 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C2×#11745183 | 2 |
| C2×#11745169 | 2 |
| C2×#11745157 | 2 |
| C2×#11745168 | 2 |
| #14271020 | 2 |
| C2×C29×#103 | 2 |
| #1788 | 29 |