Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#10596941 | C2 | semidirect |
| 2. C2×D296 | C2 | semidirect |
| 3. C2×#10596939 | C2 | semidirect |
| 4. #11924532 | C2 | semidirect |
| 5. #11924525 | C2 | semidirect |
| 6. #11924446 | C2 | semidirect |
| 7. C2×SD16×C37 | C2 | semidirect |
| 36. C8×C37 | D4 | semidirect |
| 37. #64436 | D4 | semidirect |
| 55. C37 | #496 | semidirect |
| 57. C2×SD16 | D37 | semidirect |
| 92. C8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596941 | 2 |
| C2×D296 | 2 |
| C2×#10596939 | 2 |
| #11924532 | 2 |
| #11924525 | 2 |
| #11924446 | 2 |
| C2×SD16×C37 | 2 |
| #496 | 37 |