Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 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. #26042359 | C2 | direct (N × H) |
| 2. C2×#19153904 | C2 | semidirect |
| 3. C2×D181⋊M16 | C2 | semidirect |
| 5. #19153904 | C22 | semidirect |
| 6. C2×#15668459 | C22 | semidirect |
| 7. D181⋊M16 | C22 | semidirect |
| 9. C2×D181⋊C8 | C22 | semidirect |
| 17. #15668459 | C23 | semidirect |
| 19. D181⋊C8 | C23 | semidirect |
| 62. C2×C181 | #568 | semidirect |
| 65. C181 | C2×#568 | semidirect |
| 129. C2 | #26042359 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042359 | 2 |
| C2×#19153904 | 2 |
| C2×D181⋊M16 | 2 |
| C22×#15668450 | 2 |
| C2×#568 | 181 |