Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19153849 | C2 | semidirect |
| 3. C2×#19153795 | C2 | semidirect |
| 4. #26041443 | C2 | semidirect |
| 5. #26041437 | C2 | semidirect |
| 6. #26041432 | C2 | semidirect |
| 7. #26041281 | C2 | semidirect |
| 8. #407×C181 | C2 | semidirect |
| 15. C22×Dic362 | C22 | semidirect |
| 20. C2×Dic724 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 25. #19153795 | C22 | semidirect |
| 26. C2×C4⋊Dic181 | C22 | semidirect |
| 29. #19153741 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. C2×M16×C181 | C22 | semidirect |
| 34. C22⋊C8×C181 | C22 | semidirect |
| 126. C22×C181 | #137 | semidirect |
| 146. C181 | #3007 | semidirect |
| 155. #407 | D181 | semidirect |
| 170. C2×M16 | C2×D181 | semidirect |
| 181. C22⋊C8 | C2×D181 | semidirect |
| 277. C22 | #19153849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C2×#19153849 | 2 |
| C2×#19153795 | 2 |
| #26041443 | 2 |
| #26041437 | 2 |
| #26041432 | 2 |
| #26041281 | 2 |
| #407×C181 | 2 |
| #3007 | 181 |