Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#20296312 | C2 | semidirect |
| 3. C22⋊(C439⋊C8) | C2 | semidirect |
| 4. (C2×D439)⋊C8 | C2 | semidirect |
| 5. C22⋊C8×C439 | C2 | semidirect |
| 14. C2×C439⋊C8 | C22 | semidirect |
| 16. C2×C8×C439 | C22 | semidirect |
| 37. C22×C439 | M16 | semidirect |
| 45. C2×D439 | M16 | semidirect |
| 56. C439 | #407 | semidirect |
| 62. C22⋊C8 | D439 | semidirect |
| 73. C2×C8 | C2×D439 | semidirect |
| 101. C22 | #20296312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D439 | 2 |
| C2×#20296312 | 2 |
| C22⋊(C439⋊C8) | 2 |
| (C2×D439)⋊C8 | 2 |
| C22⋊C8×C439 | 2 |
| #407 | 439 |