Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041910 | C2 | semidirect |
| 3. #26041581 | C2 | semidirect |
| 4. #26041577 | C2 | semidirect |
| 5. #26041567 | C2 | semidirect |
| 6. #26041557 | C2 | semidirect |
| 7. #26041319 | C2 | semidirect |
| 8. #26041317 | C2 | semidirect |
| 9. #26041305 | C2 | semidirect |
| 14. #19153815 | C22 | semidirect |
| 16. #19153807 | C22 | semidirect |
| 26. #19153750 | C22 | semidirect |
| 27. #19153750 | C22 | semidirect |
| 28. #19153749 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. #19153748 | C22 | semidirect |
| 31. #19153747 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153745 | C22 | semidirect |
| 66. C2×D4×C181 | Q8 | semidirect |
| 124. C181 | #3081 | semidirect |
| 170. C2×D4 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041910 | 2 |
| #26041754 | 2 |
| #26041581 | 2 |
| #26041577 | 2 |
| #26041567 | 2 |
| #26041557 | 2 |
| #26041319 | 2 |
| #26041317 | 2 |
| #26041305 | 2 |
| #26041284 | 2 |
| C2×#102×C181 | 2 |
| #3081 | 181 |