Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
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. #26045823 | C2 | semidirect |
| 3. #26045798 | C2 | semidirect |
| 4. #26045728 | C2 | semidirect |
| 5. #26045711 | C2 | semidirect |
| 6. #26045709 | C2 | semidirect |
| 7. C2×SD16×C373 | C2 | semidirect |
| 51. C373 | #471 | semidirect |
| 55. C2×SD16 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045823 | 2 |
| #26045818 | 2 |
| #26045798 | 2 |
| #26045728 | 2 |
| #26045711 | 2 |
| #26045709 | 2 |
| C2×SD16×C373 | 2 |
| #471 | 373 |