Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041994 | C2 | semidirect |
| 2. D4×D724 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041604 | C2 | semidirect |
| 5. #26041570 | C2 | semidirect |
| 6. #26041532 | C2 | semidirect |
| 7. #26041475 | C2 | semidirect |
| 8. #26041415 | C2 | semidirect |
| 9. C4×D1448 | C2 | semidirect |
| 10. #26041285 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 15. C2×D1448 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 21. #19153790 | C22 | semidirect |
| 25. C4×D724 | C22 | semidirect |
| 26. #19153775 | C22 | semidirect |
| 28. #19153750 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 32. #19153738 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 35. #19153738 | C22 | semidirect |
| 36. C2×M16×C181 | C22 | semidirect |
| 38. C4⋊C8×C181 | C22 | semidirect |
| 39. C22⋊C8×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 140. C181 | #3325 | semidirect |
| 151. #436 | D181 | semidirect |
| 157. C2×M16 | C2×D181 | semidirect |
| 173. C4⋊C8 | C2×D181 | semidirect |
| 180. C22⋊C8 | C2×D181 | semidirect |
| 181. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| D4×D724 | 2 |
| #26041626 | 2 |
| #26041604 | 2 |
| #26041570 | 2 |
| #26041532 | 2 |
| #26041475 | 2 |
| #26041415 | 2 |
| C4×D1448 | 2 |
| #26041285 | 2 |
| #436×C181 | 2 |
| #3325 | 181 |