Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #11924569 | C2 | semidirect |
| 3. C2×#10596930 | C2 | semidirect |
| 4. #11924542 | C2 | semidirect |
| 5. #11924454 | C2 | semidirect |
| 6. #11924452 | C2 | semidirect |
| 7. #108×C37 | C2 | semidirect |
| 52. C37 | #471 | semidirect |
| 57. #108 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924569 | 2 |
| #11924564 | 2 |
| C2×#10596930 | 2 |
| #11924542 | 2 |
| #11924454 | 2 |
| #11924452 | 2 |
| #108×C37 | 2 |
| #471 | 37 |