Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153846 | C2 | semidirect |
| 2. C22×#15668437 | C2 | semidirect |
| 3. C2×#19153823 | C2 | semidirect |
| 4. #26041540 | C2 | direct (N × H) |
| 5. C2×#19153751 | C2 | semidirect |
| 6. C2×#19153734 | C2 | semidirect |
| 7. C2×#19153733 | C2 | semidirect |
| 11. #19153846 | C22 | semidirect |
| 17. C2×#15668437 | C22 | semidirect |
| 19. #19153823 | C22 | semidirect |
| 25. #19153751 | C22 | semidirect |
| 26. #19153734 | C22 | semidirect |
| 27. #19153733 | C22 | semidirect |
| 136. C2×C181 | #471 | semidirect |
| 138. C181 | C2×#471 | semidirect |
| 275. C2 | #26041540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153846 | 2 |
| C22×#15668437 | 2 |
| C2×#19153823 | 2 |
| #26041540 | 2 |
| C2×#19153751 | 2 |
| C2×#19153734 | 2 |
| C2×#19153733 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| C2×#471 | 181 |