Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D37⋊M16 | C2 | semidirect |
| 2. #11924615 | C2 | semidirect |
| 3. #11924601 | C2 | semidirect |
| 5. C2×Q8×C37 | C4 | semidirect |
| 8. #10596966 | C4 | semidirect |
| 11. C2×D148 | C4 | semidirect |
| 17. C4×#3866 | C22 | semidirect |
| 18. #10596953 | C22 | semidirect |
| 57. C37 | #421 | semidirect |
| 66. C2×Q8 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D37⋊M16 | 2 |
| #11924615 | 2 |
| #11924601 | 2 |
| C2×#10596966 | 2 |
| #421 | 37 |