Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1976 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×D724 | C2 | semidirect |
| 2. C22×#15668434 | C2 | direct (N × H) |
| 3. C23×#13089678 | C2 | semidirect |
| 4. C23×D4×C181 | C2 | semidirect |
| 7. C22×D724 | C22 | semidirect |
| 8. C2×#15668434 | C22 | direct (N × H) |
| 9. C22×#13089678 | C22 | semidirect |
| 12. C22×D4×C181 | C22 | semidirect |
| 17. C2×D724 | C23 | semidirect |
| 18. #15668434 | C23 | direct (N × H) |
| 19. C2×#13089678 | C23 | semidirect |
| 24. C2×D4×C181 | C23 | semidirect |
| 30. D724 | C24 | semidirect |
| 31. #13089678 | C24 | semidirect |
| 34. C23×C181 | D8 | semidirect |
| 37. D4×C181 | C24 | semidirect |
| 42. C22×C181 | C2×D8 | semidirect |
| 49. C2×C181 | C22×D8 | semidirect |
| 52. C181 | C23×D8 | semidirect |
| 55. C23×D4 | D181 | semidirect |
| 63. C22×D4 | C2×D181 | semidirect |
| 75. C2×D4 | C22×D181 | semidirect |
| 84. C23 | #15668434 | direct (N × H) |
| 89. D4 | C23×D181 | semidirect |
| 97. C22 | C2×#15668434 | direct (N × H) |
| 103. C2 | C22×#15668434 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D724 | 2 |
| C22×#15668434 | 2 |
| C23×#13089678 | 2 |
| C23×D4×C181 | 2 |
| C23×D8 | 181 |