Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #26041883 | C2 | direct (N × H) |
| 2. C2×#19153808 | C2 | semidirect |
| 3. C2×#19153797 | C2 | semidirect |
| 4. C2×#19153788 | C2 | semidirect |
| 5. C2×#19153787 | C2 | semidirect |
| 6. C2×D4×Dic181 | C2 | semidirect |
| 7. C2×#19153773 | C2 | semidirect |
| 8. C2×#127×C181 | C2 | semidirect |
| 12. #19153808 | C22 | semidirect |
| 13. #19153797 | C22 | semidirect |
| 14. #19153788 | C22 | semidirect |
| 15. #19153787 | C22 | semidirect |
| 16. D4×Dic181 | C22 | semidirect |
| 17. #19153773 | C22 | semidirect |
| 27. #127×C181 | C22 | semidirect |
| 93. C2×C181 | #540 | semidirect |
| 97. C181 | C2×#540 | semidirect |
| 100. C2×#127 | D181 | semidirect |
| 112. #127 | C2×D181 | semidirect |
| 192. C2 | #26041883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041883 | 2 |
| C2×#19153808 | 2 |
| C2×#19153797 | 2 |
| C2×#19153788 | 2 |
| C2×#19153787 | 2 |
| C2×D4×Dic181 | 2 |
| C2×#19153773 | 2 |
| C2×#127×C181 | 2 |
| C2×#540 | 181 |