Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#19153863 | C2 | semidirect |
| 2. #26042077 | C2 | semidirect |
| 3. #26041850 | C2 | semidirect |
| 4. #26041460 | C2 | semidirect |
| 5. #26041450 | C2 | semidirect |
| 6. #26041296 | C2 | semidirect |
| 7. #26041295 | C2 | semidirect |
| 8. C2×#19153734 | C2 | semidirect |
| 9. #575×C181 | C2 | semidirect |
| 21. #19153847 | C22 | semidirect |
| 23. #19153842 | C22 | semidirect |
| 27. #19153814 | C22 | semidirect |
| 28. #19153803 | C22 | semidirect |
| 32. #19153743 | C22 | semidirect |
| 33. #19153742 | C22 | semidirect |
| 34. #19153734 | C22 | semidirect |
| 38. #137×C181 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C181 | C22 | semidirect |
| 185. C181 | #3020 | semidirect |
| 189. #575 | D181 | semidirect |
| 212. #137 | C2×D181 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| #26042077 | 2 |
| #26041850 | 2 |
| #26041460 | 2 |
| #26041450 | 2 |
| #26041296 | 2 |
| #26041295 | 2 |
| C2×#19153734 | 2 |
| #575×C181 | 2 |
| #3020 | 181 |