Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
124 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 55 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×#10596929 | C2 | semidirect |
| 3. #11924465 | C2 | semidirect |
| 4. C22⋊#64436 | C2 | semidirect |
| 5. #11924448 | C2 | semidirect |
| 6. #11924446 | C2 | semidirect |
| 7. C22×C8×C37 | C2 | semidirect |
| 34. C8×C37 | D4 | semidirect |
| 39. C22×C37 | M16 | semidirect |
| 56. C37 | #435 | semidirect |
| 58. C22×C8 | D37 | semidirect |
| 92. C8 | C22⋊D37 | semidirect |
| 98. C22 | #10596929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596929 | 2 |
| C4×C22⋊D37 | 2 |
| #11924465 | 2 |
| C22⋊#64436 | 2 |
| #11924448 | 2 |
| #11924446 | 2 |
| C22×C8×C37 | 2 |
| #435 | 37 |