Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19153775 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041610 | C2 | semidirect |
| 6. #26041604 | C2 | semidirect |
| 7. #26041598 | C2 | semidirect |
| 8. #26041593 | C2 | semidirect |
| 9. #26041317 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. C2×C22⋊C8×C181 | C2 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153750 | C22 | semidirect |
| 32. #19153748 | C22 | semidirect |
| 33. #19153748 | C22 | semidirect |
| 34. #19153741 | C22 | semidirect |
| 35. #19153741 | C22 | semidirect |
| 36. #19153738 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 143. C181 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041790 | 2 |
| C2×#19153775 | 2 |
| #26041621 | 2 |
| #26041615 | 2 |
| #26041610 | 2 |
| #26041604 | 2 |
| #26041598 | 2 |
| #26041593 | 2 |
| #26041317 | 2 |
| #26041276 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #3091 | 181 |