Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26045787 | C2 | semidirect |
| 2. #26045783 | C2 | semidirect |
| 3. #26045781 | C2 | semidirect |
| 4. #26045777 | C2 | semidirect |
| 5. #26045768 | C2 | semidirect |
| 7. C4×D1492 | C2 | semidirect |
| 8. C4×D1492 | C2 | semidirect |
| 9. #26045749 | C2 | semidirect |
| 10. C42×D373 | C2 | semidirect |
| 11. C4×Q8×C373 | C2 | semidirect |
| 74. C373 | #529 | semidirect |
| 82. C4×Q8 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045787 | 2 |
| #26045783 | 2 |
| #26045781 | 2 |
| #26045777 | 2 |
| #26045768 | 2 |
| #26045767 | 2 |
| C4×D1492 | 2 |
| #26045749 | 2 |
| C42×D373 | 2 |
| C4×Q8×C373 | 2 |
| #529 | 373 |