Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11924501 | C2 | semidirect |
| 4. #11924459 | C2 | semidirect |
| 6. C8×Dic37 | C2 | semidirect |
| 7. #106×C37 | C2 | semidirect |
| 19. #10596930 | C4 | semidirect |
| 31. Dic74 | C2×C4 | semidirect |
| 32. C8×C37 | C2×C4 | semidirect |
| 44. Dic37 | SD16 | semidirect |
| 50. C37 | C4×SD16 | semidirect |
| 54. #106 | D37 | semidirect |
| 83. C8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596930 | 2 |
| #11924501 | 2 |
| #11924498 | 2 |
| #11924459 | 2 |
| #11924456 | 2 |
| C8×Dic37 | 2 |
| #106×C37 | 2 |
| C4×SD16 | 37 |