Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 3. #11924469 | C2 | semidirect |
| 4. #11924460 | C2 | semidirect |
| 6. #11924447 | C2 | semidirect |
| 7. C4×Q8×C37 | C2 | semidirect |
| 15. #10596941 | C4 | semidirect |
| 22. Q8×C37 | C2×C4 | semidirect |
| 33. #64436 | C2×C4 | semidirect |
| 50. C37 | #440 | semidirect |
| 52. C4×Q8 | D37 | semidirect |
| 72. Q8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596941 | 2 |
| C4×D148 | 2 |
| #11924469 | 2 |
| #11924460 | 2 |
| #11924456 | 2 |
| #11924447 | 2 |
| C4×Q8×C37 | 2 |
| #440 | 37 |