Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 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. #26041891 | C2 | direct (N × H) |
| 2. C2×#19153816 | C2 | semidirect |
| 4. C2×#19153808 | C2 | semidirect |
| 5. C2×#19153806 | C2 | semidirect |
| 7. C2×C4×Dic362 | C2 | semidirect |
| 10. #19153816 | C22 | semidirect |
| 12. #19153808 | C22 | semidirect |
| 13. #19153806 | C22 | semidirect |
| 15. C4×Dic362 | C22 | semidirect |
| 82. C2×C181 | #541 | semidirect |
| 85. C181 | C2×#541 | semidirect |
| 168. C2 | #26041891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041891 | 2 |
| C2×#19153816 | 2 |
| C2×#19153809 | 2 |
| C2×#19153808 | 2 |
| C2×#19153806 | 2 |
| C2×#19153795 | 2 |
| C2×C4×Dic362 | 2 |
| C2×#117×C181 | 2 |
| C2×#541 | 181 |