Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #26042358 | C2 | semidirect |
| 2. #41×#10624382 | C2 | semidirect |
| 3. #26042278 | C2 | semidirect |
| 4. #26042276 | C2 | semidirect |
| 5. C2×#19153881 | C2 | semidirect |
| 6. D181⋊#104 | C2 | semidirect |
| 10. C2×#15668459 | C22 | semidirect |
| 11. D181⋊M16 | C22 | semidirect |
| 14. #19153895 | C22 | semidirect |
| 15. C2×C4×#10624382 | C22 | semidirect |
| 16. #19153881 | C22 | semidirect |
| 17. #19153881 | C22 | semidirect |
| 18. #19153881 | C22 | semidirect |
| 19. #19153880 | C22 | semidirect |
| 20. #19153880 | C22 | semidirect |
| 22. #19153864 | C4 | semidirect |
| 24. #19153862 | C4 | semidirect |
| 25. #19153862 | C4 | semidirect |
| 31. 2−1+4×C181 | C4 | semidirect |
| 48. #15668450 | C2×C4 | semidirect |
| 55. #15668449 | C2×C4 | semidirect |
| 60. Q8×D181 | C2×C4 | semidirect |
| 64. C2×D724 | C2×C4 | semidirect |
| 68. D4×D181 | C2×C4 | semidirect |
| 75. #41×C181 | C2×C4 | semidirect |
| 77. C2×Q8×C181 | C2×C4 | semidirect |
| 139. C181 | #2901 | semidirect |
| 150. 2−1+4 | #10624382 | semidirect |
| 189. #41 | C2×#10624382 | semidirect |
| 194. C2×Q8 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042358 | 2 |
| #41×#10624382 | 2 |
| #26042278 | 2 |
| #26042276 | 2 |
| C2×#19153881 | 2 |
| D181⋊#104 | 2 |
| #26042116 | 2 |
| #2901 | 181 |