Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 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 |
| 3. Q8×Dic37 | C2 | semidirect |
| 4. #11924465 | C2 | semidirect |
| 5. #11924458 | C2 | semidirect |
| 6. #11924457 | C2 | semidirect |
| 7. C2×SD16×C37 | C2 | semidirect |
| 24. Q8×C37 | D4 | semidirect |
| 50. Dic37 | SD16 | semidirect |
| 57. C37 | #460 | semidirect |
| 59. C2×SD16 | D37 | semidirect |
| 81. Q8 | 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 |
| #11924532 | 2 |
| Q8×Dic37 | 2 |
| #11924465 | 2 |
| #11924458 | 2 |
| #11924457 | 2 |
| C2×SD16×C37 | 2 |
| #460 | 37 |