Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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. D37⋊M16 | C2 | direct (N × H) |
| 3. C2×#10596957 | C2 | semidirect |
| 4. C2×D37⋊C8 | C2 | semidirect |
| 15. #10596957 | C22 | semidirect |
| 16. C2×#64438 | C22 | semidirect |
| 17. #10596953 | C22 | semidirect |
| 18. D37⋊C8 | C22 | semidirect |
| 37. #64438 | C23 | semidirect |
| 43. C2×D37 | M16 | semidirect |
| 52. C2×C37 | C2×M16 | semidirect |
| 55. D37 | C2×M16 | semidirect |
| 57. C37 | C22×M16 | semidirect |
| 111. C2 | D37⋊M16 | 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 |
| D37⋊M16 | 2 |
| C2×#10596957 | 2 |
| C2×D37⋊C8 | 2 |
| C22×C4×D37 | 2 |
| C22×M16 | 37 |