Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. C2×#10596953 | C2 | semidirect |
| 2. C2×C4×#3866 | C2 | semidirect |
| 3. #11924600 | C2 | direct (N × H) |
| 6. C2×D4×C37 | C4 | semidirect |
| 11. #10596964 | C4 | semidirect |
| 14. C2×Dic74 | C4 | semidirect |
| 17. C4×#3866 | C22 | semidirect |
| 19. #10596953 | C22 | semidirect |
| 25. D4×C37 | C2×C4 | semidirect |
| 38. Dic74 | C2×C4 | semidirect |
| 53. C2×C37 | #104 | semidirect |
| 58. C37 | C2×#104 | semidirect |
| 69. C2×D4 | #3866 | semidirect |
| 85. D4 | C2×#3866 | semidirect |
| 113. C2 | #11924600 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596953 | 2 |
| C2×C4×#3866 | 2 |
| #11924600 | 2 |
| C2×#10596964 | 2 |
| C2×#104 | 37 |