Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 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. C4×D1492 | C2 | semidirect |
| 3. #26045723 | C2 | semidirect |
| 4. #26045713 | C2 | semidirect |
| 5. #26045712 | C2 | semidirect |
| 6. #26045703 | C2 | semidirect |
| 7. C4×D4×C373 | C2 | semidirect |
| 10. #20238595 | C4 | semidirect |
| 22. D1492 | C2×C4 | semidirect |
| 26. #15688412 | C2×C4 | semidirect |
| 29. D4×C373 | C2×C4 | semidirect |
| 53. C373 | #442 | semidirect |
| 57. C4×D4 | D373 | semidirect |
| 79. D4 | C4×D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238595 | 2 |
| C4×D1492 | 2 |
| #26045723 | 2 |
| #26045713 | 2 |
| #26045712 | 2 |
| #26045703 | 2 |
| C4×D4×C373 | 2 |
| #442 | 373 |