Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C22×C4×D431 | C2 | semidirect |
| 3. C4×D1724 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic431 | C2 | semidirect |
| 5. C2×(C2×D431)⋊C4 | C2 | semidirect |
| 6. C2×C42×C431 | C2 | semidirect |
| 8. C2×D1724 | C4 | direct (N × H) |
| 12. C2×C4×D431 | C22 | semidirect |
| 13. C4⋊Dic431 | C22 | semidirect |
| 14. (C2×D431)⋊C4 | C22 | semidirect |
| 18. C42×C431 | C22 | semidirect |
| 21. C22×D431 | C2×C4 | semidirect |
| 23. D1724 | C2×C4 | direct (N × H) |
| 29. C2×C4×C431 | C2×C4 | semidirect |
| 30. C2×C4×C431 | D4 | semidirect |
| 41. C2×D431 | C22×C4 | semidirect |
| 43. C4×C431 | C22×C4 | semidirect |
| 44. C4×C431 | C2×D4 | semidirect |
| 46. C2×C431 | C4×D4 | semidirect |
| 51. C431 | C2×C4×D4 | semidirect |
| 58. C2×C42 | D431 | semidirect |
| 70. C42 | C2×D431 | semidirect |
| 81. C2×C4 | C4×D431 | semidirect |
| 82. C2×C4 | D1724 | direct (N × H) |
| 96. C4 | C2×C4×D431 | semidirect |
| 97. C4 | C2×D1724 | direct (N × H) |
| 99. C2 | C4×D1724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1724 | 2 |
| C22×C4×D431 | 2 |
| C4×D1724 | 2 |
| C2×C4⋊Dic431 | 2 |
| C2×(C2×D431)⋊C4 | 2 |
| C2×C42×C431 | 2 |
| C2×C4×D4 | 431 |