Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153863 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. C22×#15668438 | C2 | semidirect |
| 4. #26041843 | C2 | semidirect |
| 5. #26041426 | C2 | semidirect |
| 6. #26041420 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 8. #26041276 | C2 | semidirect |
| 9. #408×C181 | C2 | semidirect |
| 13. C2×#15668449 | C22 | semidirect |
| 17. C22×Dic362 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 31. #19153741 | C22 | semidirect |
| 32. #19153738 | C22 | semidirect |
| 36. C22⋊C8×C181 | C22 | semidirect |
| 41. #15668449 | D4 | semidirect |
| 49. C2×Dic362 | D4 | semidirect |
| 145. C181 | #3010 | semidirect |
| 155. #408 | D181 | semidirect |
| 182. C22⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| C2×#19153844 | 2 |
| C22×#15668438 | 2 |
| #26041843 | 2 |
| #26041426 | 2 |
| #26041420 | 2 |
| #26041289 | 2 |
| #26041276 | 2 |
| #408×C181 | 2 |
| #3010 | 181 |