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×#15668438 | C2 | semidirect |
| 3. #26041850 | C2 | semidirect |
| 4. #26041753 | C2 | semidirect |
| 5. #26041493 | C2 | semidirect |
| 6. #26041483 | C2 | semidirect |
| 7. #26041305 | C2 | semidirect |
| 8. #26041287 | C2 | semidirect |
| 9. #416×C181 | C2 | semidirect |
| 18. #19153814 | C22 | semidirect |
| 19. #19153803 | C22 | semidirect |
| 26. #19153745 | C22 | semidirect |
| 27. #19153739 | C22 | semidirect |
| 31. #103×C181 | C22 | semidirect |
| 32. #102×C181 | C22 | semidirect |
| 116. C181 | #3042 | semidirect |
| 126. #416 | D181 | semidirect |
| 148. #103 | C2×D181 | semidirect |
| 149. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C22×#15668438 | 2 |
| #26041850 | 2 |
| #26041753 | 2 |
| #26041493 | 2 |
| #26041483 | 2 |
| #26041305 | 2 |
| #26041287 | 2 |
| #416×C181 | 2 |
| #3042 | 181 |