Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#15668436 | C2 | semidirect |
| 3. #26041853 | C2 | semidirect |
| 4. #26041753 | C2 | semidirect |
| 5. #26041497 | C2 | semidirect |
| 6. #26041483 | C2 | semidirect |
| 7. #26041307 | C2 | semidirect |
| 8. #26041273 | C2 | semidirect |
| 9. #419×C181 | C2 | semidirect |
| 18. #19153814 | C22 | semidirect |
| 19. #19153805 | C22 | semidirect |
| 26. #19153745 | C22 | semidirect |
| 27. #19153739 | C22 | semidirect |
| 28. #19153736 | C22 | semidirect |
| 32. #103×C181 | C22 | semidirect |
| 116. C181 | #3042 | semidirect |
| 125. #419 | D181 | semidirect |
| 148. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C22×#15668436 | 2 |
| #26041853 | 2 |
| #26041753 | 2 |
| #26041497 | 2 |
| #26041483 | 2 |
| #26041307 | 2 |
| #26041273 | 2 |
| #419×C181 | 2 |
| #3042 | 181 |