Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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. #26042096 | C2 | direct (N × H) |
| 3. C2×#19153849 | C2 | semidirect |
| 4. C2×#19153838 | C2 | semidirect |
| 5. C22×Dic724 | C2 | semidirect |
| 6. C2×#131×C181 | C2 | semidirect |
| 8. #19153863 | C22 | semidirect |
| 13. #19153849 | C22 | semidirect |
| 14. #19153838 | C22 | semidirect |
| 17. C2×Dic724 | C22 | semidirect |
| 21. #131×C181 | C22 | semidirect |
| 78. C2×C181 | #578 | semidirect |
| 81. C181 | C2×#578 | semidirect |
| 88. C2×#131 | D181 | semidirect |
| 103. #131 | C2×D181 | semidirect |
| 161. C2 | #26042096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| #26042096 | 2 |
| C2×#19153849 | 2 |
| C2×#19153838 | 2 |
| C22×Dic724 | 2 |
| C2×#131×C181 | 2 |
| C2×#578 | 181 |