Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19153847 | C2 | semidirect |
| 3. C4×#15668449 | C2 | semidirect |
| 4. #26041498 | C2 | semidirect |
| 5. #26041491 | C2 | semidirect |
| 6. #26041303 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 8. #26041284 | C2 | semidirect |
| 9. C2×#124×C181 | C2 | semidirect |
| 13. C2×#15668439 | C22 | semidirect |
| 15. C2×#15668436 | C22 | semidirect |
| 19. C4×Dic362 | C22 | semidirect |
| 20. C4×D724 | C22 | semidirect |
| 25. C4⋊#13089678 | C22 | semidirect |
| 26. #19153740 | C22 | semidirect |
| 125. C181 | #3040 | semidirect |
| 129. C2×#124 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153842 | 2 |
| C4×#15668449 | 2 |
| #26041498 | 2 |
| #26041491 | 2 |
| #26041303 | 2 |
| #26041288 | 2 |
| #26041284 | 2 |
| C2×#124×C181 | 2 |
| #3040 | 181 |