Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
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×D692 | C2 | semidirect |
| 2. C22×#14583811 | C2 | direct (N × H) |
| 3. C23×#13063436 | C2 | semidirect |
| 4. C23×D4×C173 | C2 | semidirect |
| 7. C22×D692 | C22 | semidirect |
| 8. C2×#14583811 | C22 | direct (N × H) |
| 9. C22×#13063436 | C22 | semidirect |
| 12. C22×D4×C173 | C22 | semidirect |
| 17. C2×D692 | C23 | semidirect |
| 18. #14583811 | C23 | direct (N × H) |
| 19. C2×#13063436 | C23 | semidirect |
| 24. C2×D4×C173 | C23 | semidirect |
| 30. D692 | C24 | semidirect |
| 31. #13063436 | C24 | semidirect |
| 34. C23×C173 | D8 | semidirect |
| 37. D4×C173 | C24 | semidirect |
| 42. C22×C173 | C2×D8 | semidirect |
| 49. C2×C173 | C22×D8 | semidirect |
| 52. C173 | C23×D8 | semidirect |
| 55. C23×D4 | D173 | semidirect |
| 63. C22×D4 | C2×D173 | semidirect |
| 75. C2×D4 | C22×D173 | semidirect |
| 84. C23 | #14583811 | direct (N × H) |
| 89. D4 | C23×D173 | semidirect |
| 97. C22 | C2×#14583811 | direct (N × H) |
| 103. C2 | C22×#14583811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C22×#14583811 | 2 |
| C23×#13063436 | 2 |
| C23×D4×C173 | 2 |
| C23×D8 | 173 |