Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #26045800 | C2 | semidirect |
| 3. #26045799 | C2 | semidirect |
| 4. #26045727 | C2 | semidirect |
| 5. #26045720 | C2 | semidirect |
| 6. C4×#15688412 | C2 | semidirect |
| 7. #104×C373 | C2 | semidirect |
| 9. #20238600 | C4 | semidirect |
| 10. #20238598 | C4 | semidirect |
| 11. #20238597 | C4 | semidirect |
| 12. #20238595 | C4 | semidirect |
| 51. C373 | #443 | semidirect |
| 58. #104 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045812 | 2 |
| #26045800 | 2 |
| #26045799 | 2 |
| #26045727 | 2 |
| #26045720 | 2 |
| C4×#15688412 | 2 |
| #104×C373 | 2 |
| #443 | 373 |