Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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. #14271210 | C2 | direct (N × H) |
| 4. C2×#11745167 | C2 | semidirect |
| 5. C2×#11745170 | C2 | semidirect |
| 6. C2×C29×#108 | C2 | semidirect |
| 19. C29×#108 | C22 | semidirect |
| 20. #11745170 | C22 | semidirect |
| 21. #11745167 | C22 | semidirect |
| 87. C2×#108 | D29 | semidirect |
| 90. C2×C29 | #430 | semidirect |
| 107. #108 | C2×D29 | semidirect |
| 108. C29 | C2×#430 | semidirect |
| 171. C2 | #14271210 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×M16×D29 | 2 |
| #14271210 | 2 |
| C2×#11745167 | 2 |
| C2×#11745170 | 2 |
| C2×C29×#108 | 2 |
| C2×#430 | 29 |