Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14271225 | C2 | semidirect |
| 3. #14271222 | C2 | semidirect |
| 4. #14271186 | C2 | semidirect |
| 6. C4×#90777 | C2 | semidirect |
| 7. C4×M16×C29 | C2 | semidirect |
| 18. C29×#97 | C22 | semidirect |
| 19. C4×C8×C29 | C22 | semidirect |
| 21. #11745162 | C22 | semidirect |
| 22. #11745151 | C22 | semidirect |
| 23. C4×#6597 | C22 | semidirect |
| 82. C4×M16 | D29 | semidirect |
| 100. #97 | C2×D29 | semidirect |
| 102. C4×C8 | C2×D29 | semidirect |
| 103. C29 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745234 | 2 |
| #14271225 | 2 |
| #14271222 | 2 |
| #14271186 | 2 |
| #14271126 | 2 |
| C4×#90777 | 2 |
| C4×M16×C29 | 2 |
| #2921 | 29 |