Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. #26045757 | C2 | semidirect |
| 4. #26045723 | C2 | semidirect |
| 5. #26045717 | C2 | semidirect |
| 6. C8×Dic373 | C2 | semidirect |
| 10. #20238598 | C4 | semidirect |
| 21. Dic746 | C2×C4 | semidirect |
| 27. #15688412 | C2×C4 | semidirect |
| 44. Dic373 | SD16 | semidirect |
| 49. C373 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238598 | 2 |
| #26045757 | 2 |
| D4×Dic373 | 2 |
| #26045723 | 2 |
| #26045717 | 2 |
| C8×Dic373 | 2 |
| #102×C373 | 2 |
| C4×SD16 | 373 |