Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×Dic724 | C2 | semidirect |
| 4. C2×C4×Dic362 | C2 | semidirect |
| 5. #26041502 | C2 | direct (N × H) |
| 6. C2×#19153741 | C2 | semidirect |
| 8. C2×C4⋊C8×C181 | C2 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 19. C4×Dic362 | C22 | semidirect |
| 25. #19153741 | C22 | semidirect |
| 30. C4⋊C8×C181 | C22 | semidirect |
| 110. C2×C181 | #464 | semidirect |
| 115. C181 | C2×#464 | semidirect |
| 122. C2×C4⋊C8 | D181 | semidirect |
| 144. C4⋊C8 | C2×D181 | semidirect |
| 227. C2 | #26041502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| C22×#15668438 | 2 |
| C2×#19153804 | 2 |
| C2×C4×Dic362 | 2 |
| #26041502 | 2 |
| C2×#19153741 | 2 |
| C2×#19153738 | 2 |
| C2×C4⋊C8×C181 | 2 |
| C2×#464 | 181 |