Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #26041645 | C2 | semidirect |
| 3. #26041641 | C2 | semidirect |
| 4. #26041636 | C2 | semidirect |
| 5. #26041627 | C2 | semidirect |
| 6. #26041283 | C2 | semidirect |
| 7. #26041278 | C2 | semidirect |
| 8. #26041273 | C2 | semidirect |
| 9. C2×#19153736 | C2 | semidirect |
| 10. #26041235 | C2 | semidirect |
| 11. #544×C181 | C2 | semidirect |
| 21. #19153739 | C22 | semidirect |
| 22. #19153739 | C22 | semidirect |
| 23. #19153739 | C22 | semidirect |
| 28. #19153736 | C22 | semidirect |
| 29. #19153736 | C22 | semidirect |
| 30. #19153736 | C22 | semidirect |
| 31. #19153727 | C22 | semidirect |
| 32. C4×#13089678 | C22 | semidirect |
| 34. C4⋊Q8×C181 | C22 | semidirect |
| 36. #125×C181 | C22 | semidirect |
| 135. C181 | #3136 | semidirect |
| 137. #544 | D181 | semidirect |
| 153. C4⋊Q8 | C2×D181 | semidirect |
| 156. #125 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041848 | 2 |
| #26041645 | 2 |
| #26041641 | 2 |
| #26041636 | 2 |
| #26041627 | 2 |
| #26041283 | 2 |
| #26041278 | 2 |
| #26041273 | 2 |
| C2×#19153736 | 2 |
| #26041235 | 2 |
| #544×C181 | 2 |
| #3136 | 181 |