Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #26045880 | C2 | semidirect |
| 2. #26045879 | C2 | semidirect |
| 3. #26045862 | C2 | semidirect |
| 4. #26045857 | C2 | semidirect |
| 5. #26045856 | C2 | semidirect |
| 6. C8×#13093637 | C2 | semidirect |
| 18. #20238600 | C4 | semidirect |
| 19. #20238599 | C4 | semidirect |
| 20. #20238595 | C4 | semidirect |
| 22. SD16×C373 | C4 | semidirect |
| 51. C373 | #443 | semidirect |
| 64. SD16 | #13093637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045880 | 2 |
| #26045879 | 2 |
| #26045862 | 2 |
| #26045857 | 2 |
| #26045856 | 2 |
| C8×#13093637 | 2 |
| #26045813 | 2 |
| #443 | 373 |