Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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×#19153849 | C2 | semidirect |
| 2. C22×#15668438 | C2 | semidirect |
| 4. #26041756 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041480 | C2 | semidirect |
| 7. #26041285 | C2 | semidirect |
| 8. #26041276 | C2 | semidirect |
| 9. #424×C181 | C2 | semidirect |
| 14. C2×Dic724 | C22 | semidirect |
| 17. C2×#15668438 | C22 | semidirect |
| 22. C4×Dic362 | C22 | semidirect |
| 26. #19153741 | C22 | semidirect |
| 28. #19153738 | C22 | semidirect |
| 32. C4⋊C8×C181 | C22 | semidirect |
| 38. C2×Dic362 | D4 | semidirect |
| 116. C181 | #3043 | semidirect |
| 124. #424 | D181 | semidirect |
| 146. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C22×#15668438 | 2 |
| #26041848 | 2 |
| #26041756 | 2 |
| #26041502 | 2 |
| #26041480 | 2 |
| #26041285 | 2 |
| #26041276 | 2 |
| #424×C181 | 2 |
| #3043 | 181 |