Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041834 | C2 | semidirect |
| 3. #26041641 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041638 | C2 | semidirect |
| 6. #26041635 | C2 | semidirect |
| 7. #26041632 | C2 | semidirect |
| 8. #26041286 | C2 | semidirect |
| 10. #26041231 | C2 | semidirect |
| 11. #489×C181 | C2 | semidirect |
| 15. #19153816 | C22 | semidirect |
| 16. #19153807 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 31. #19153740 | C22 | semidirect |
| 32. #19153739 | C22 | semidirect |
| 36. #19153727 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #103×C181 | C22 | semidirect |
| 42. #97×C181 | C22 | semidirect |
| 138. C181 | #3140 | semidirect |
| 145. #489 | D181 | semidirect |
| 155. C4⋊Q8 | C2×D181 | semidirect |
| 174. #103 | C2×D181 | semidirect |
| 180. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #124×D181 | 2 |
| #26041641 | 2 |
| #26041639 | 2 |
| #26041638 | 2 |
| #26041635 | 2 |
| #26041632 | 2 |
| #26041286 | 2 |
| #26041282 | 2 |
| #26041231 | 2 |
| #489×C181 | 2 |
| #3140 | 181 |