Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041829 | C2 | semidirect |
| 2. C2×C4×D724 | C2 | semidirect |
| 3. #26041598 | C2 | semidirect |
| 4. #26041570 | C2 | semidirect |
| 5. #26041475 | C2 | semidirect |
| 6. #26041415 | C2 | semidirect |
| 7. #26041392 | C2 | semidirect |
| 8. #432×C181 | C2 | semidirect |
| 13. #19153816 | C22 | semidirect |
| 14. #19153813 | C22 | semidirect |
| 23. C4×D724 | C22 | semidirect |
| 26. #19153748 | C22 | semidirect |
| 28. #19153738 | C22 | semidirect |
| 30. C4⋊C8×C181 | C22 | semidirect |
| 32. #97×C181 | C22 | semidirect |
| 76. D724 | #41 | semidirect |
| 120. C181 | #3109 | semidirect |
| 129. #432 | D181 | semidirect |
| 149. C4⋊C8 | C2×D181 | semidirect |
| 153. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| C2×C4×D724 | 2 |
| #26041598 | 2 |
| #26041570 | 2 |
| #26041475 | 2 |
| #26041415 | 2 |
| #26041392 | 2 |
| #432×C181 | 2 |
| #3109 | 181 |