Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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. #26045725 | C2 | semidirect |
| 3. #26045723 | C2 | semidirect |
| 4. #26045712 | C2 | semidirect |
| 5. #26045712 | C2 | semidirect |
| 6. C22⋊#15688412 | C2 | semidirect |
| 7. #117×C373 | C2 | semidirect |
| 51. C373 | #482 | semidirect |
| 54. #117 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045766 | 2 |
| #26045725 | 2 |
| #26045723 | 2 |
| #26045712 | 2 |
| C22⋊#15688412 | 2 |
| #117×C373 | 2 |
| #482 | 373 |