Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11745166 | C2 | semidirect |
| 3. C2×#11745164 | C2 | semidirect |
| 5. #14271069 | C2 | semidirect |
| 7. C2×C29×#97 | C2 | semidirect |
| 18. C2×#90773 | C4 | semidirect |
| 87. C8×C29 | C22⋊C4 | semidirect |
| 111. C2×#97 | D29 | semidirect |
| 136. C29 | #1973 | semidirect |
| 200. C8 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745166 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| #14271069 | 2 |
| #14271065 | 2 |
| C2×C29×#97 | 2 |
| #1973 | 29 |