Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #28352214 | C2 | semidirect |
| 2. C2×#20293785 | C2 | semidirect |
| 3. #28352196 | C2 | semidirect |
| 4. #28352124 | C2 | semidirect |
| 5. #28352106 | C2 | semidirect |
| 6. #28352105 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C431 | C2 | semidirect |
| 53. C431 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352214 | 2 |
| C2×#20293785 | 2 |
| #28352196 | 2 |
| #28352124 | 2 |
| #28352106 | 2 |
| #28352105 | 2 |
| AGL(1,ℤ/8)×C431 | 2 |
| #472 | 431 |