Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041885 | C2 | semidirect |
| 2. #26041847 | C2 | semidirect |
| 3. #26041669 | C2 | semidirect |
| 4. #26041656 | C2 | semidirect |
| 5. #26041645 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041473 | C2 | semidirect |
| 8. #26041427 | C2 | semidirect |
| 9. #26041414 | C2 | semidirect |
| 10. #26041338 | C2 | semidirect |
| 11. #488×C181 | C2 | semidirect |
| 14. C2×#15668436 | C22 | semidirect |
| 16. C2×D1448 | C22 | semidirect |
| 19. #19153813 | C22 | semidirect |
| 27. #19153778 | C22 | semidirect |
| 29. #19153745 | C22 | semidirect |
| 31. #19153736 | C22 | semidirect |
| 33. #19153727 | C22 | semidirect |
| 34. #125×C181 | C22 | semidirect |
| 36. #103×C181 | C22 | semidirect |
| 38. C4×C8×C181 | C22 | semidirect |
| 128. C181 | #3220 | semidirect |
| 135. #488 | D181 | semidirect |
| 150. #125 | C2×D181 | semidirect |
| 161. #103 | C2×D181 | semidirect |
| 167. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041885 | 2 |
| #26041847 | 2 |
| #26041669 | 2 |
| #26041656 | 2 |
| #26041645 | 2 |
| #26041497 | 2 |
| #26041473 | 2 |
| #26041427 | 2 |
| #26041414 | 2 |
| #26041338 | 2 |
| #488×C181 | 2 |
| #3220 | 181 |