Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #26041613 | C2 | semidirect |
| 4. #26041571 | C2 | semidirect |
| 5. #26041519 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 7. #26041436 | C2 | semidirect |
| 8. C4×Dic724 | C2 | semidirect |
| 10. #103×D181 | C2 | semidirect |
| 11. #487×C181 | C2 | semidirect |
| 82. D724 | Q16 | semidirect |
| 122. C181 | #3299 | semidirect |
| 126. #487 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| #26041944 | 2 |
| #26041613 | 2 |
| #26041571 | 2 |
| #26041519 | 2 |
| #26041486 | 2 |
| #26041436 | 2 |
| C4×Dic724 | 2 |
| C8×D724 | 2 |
| #103×D181 | 2 |
| #487×C181 | 2 |
| #3299 | 181 |