Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19153796 | C2 | semidirect |
| 3. #26041622 | C2 | semidirect |
| 4. #26041597 | C2 | semidirect |
| 5. #26041536 | C2 | semidirect |
| 6. #26041526 | C2 | semidirect |
| 7. #26041444 | C2 | semidirect |
| 8. #26041434 | C2 | semidirect |
| 9. #26041420 | C2 | semidirect |
| 10. #26041241 | C2 | semidirect |
| 11. #484×C181 | C2 | semidirect |
| 15. C2×#15668439 | C22 | semidirect |
| 16. C2×#15668438 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 149. C181 | #3196 | semidirect |
| 154. #484 | D181 | semidirect |
| 184. #107 | C2×D181 | semidirect |
| 188. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041792 | 2 |
| C2×#19153796 | 2 |
| #26041622 | 2 |
| #26041597 | 2 |
| #26041536 | 2 |
| #26041526 | 2 |
| #26041444 | 2 |
| #26041434 | 2 |
| #26041420 | 2 |
| #26041241 | 2 |
| #484×C181 | 2 |
| #3196 | 181 |