Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26045777 | C2 | semidirect |
| 4. #26045776 | C2 | semidirect |
| 5. #26045768 | C2 | semidirect |
| 7. #26045752 | C2 | semidirect |
| 8. C2×#20238589 | C2 | semidirect |
| 9. C22⋊Q8×C373 | C2 | semidirect |
| 66. C373 | #539 | semidirect |
| 73. C22⋊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 |
| #26045777 | 2 |
| #26045776 | 2 |
| #26045768 | 2 |
| #26045766 | 2 |
| #26045752 | 2 |
| C2×#20238589 | 2 |
| C22⋊Q8×C373 | 2 |
| #539 | 373 |