Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19153844 | C2 | semidirect |
| 2. C2×#19153838 | C2 | semidirect |
| 3. C22×D1448 | C2 | semidirect |
| 4. #26041848 | C2 | semidirect |
| 5. #26041668 | C2 | semidirect |
| 6. #26041663 | C2 | semidirect |
| 7. #26041656 | C2 | semidirect |
| 8. #405×C181 | C2 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 14. C2×#15668438 | C22 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 19. C2×D1448 | C22 | semidirect |
| 20. C2×D1448 | C22 | semidirect |
| 21. #19153813 | C22 | semidirect |
| 22. #19153804 | C22 | semidirect |
| 28. #97×C181 | C22 | semidirect |
| 29. C4×C8×C181 | C22 | semidirect |
| 51. M16×C181 | D4 | semidirect |
| 52. C2×C8×C181 | D4 | semidirect |
| 101. C181 | #3155 | semidirect |
| 110. #405 | D181 | semidirect |
| 130. #97 | C2×D181 | semidirect |
| 131. C4×C8 | C2×D181 | semidirect |
| 152. M16 | D724 | semidirect |
| 153. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153838 | 2 |
| C22×D1448 | 2 |
| #26041848 | 2 |
| #26041668 | 2 |
| #26041663 | 2 |
| #26041656 | 2 |
| #405×C181 | 2 |
| #3155 | 181 |