Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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. #28352171 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic431 | C2 | semidirect |
| 5. C2×Dic431⋊C4 | C2 | semidirect |
| 6. C2×C22⋊Dic431 | C2 | semidirect |
| 7. C2×(C2×D431)⋊C4 | C2 | semidirect |
| 8. C2×C22⋊C4×C431 | C2 | semidirect |
| 16. C2×C4×D431 | C22 | semidirect |
| 17. C4⋊Dic431 | C22 | semidirect |
| 18. Dic431⋊C4 | C22 | semidirect |
| 19. C22⋊Dic431 | C22 | semidirect |
| 20. (C2×D431)⋊C4 | C22 | semidirect |
| 24. C22⋊C4×C431 | C22 | semidirect |
| 64. C2×C431 | #123 | semidirect |
| 69. C431 | C2×#123 | semidirect |
| 78. C2×C22⋊C4 | D431 | semidirect |
| 94. C22⋊C4 | C2×D431 | semidirect |
| 135. C2 | #28352171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D431 | 2 |
| C22×C4×D431 | 2 |
| #28352171 | 2 |
| C2×C4⋊Dic431 | 2 |
| C2×Dic431⋊C4 | 2 |
| C2×C22⋊Dic431 | 2 |
| C2×(C2×D431)⋊C4 | 2 |
| C2×C22⋊C4×C431 | 2 |
| C2×#123 | 431 |