Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#20296316 | C2 | semidirect |
| 2. C2×#20296313 | C2 | semidirect |
| 4. #28380676 | C2 | semidirect |
| 5. #28380667 | C2 | semidirect |
| 6. #28380663 | C2 | semidirect |
| 7. C22⋊Q8×C439 | C2 | semidirect |
| 27. C439⋊C8 | D4 | semidirect |
| 55. C439 | #468 | semidirect |
| 59. C22⋊Q8 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296316 | 2 |
| C2×#20296313 | 2 |
| #28380717 | 2 |
| #28380676 | 2 |
| #28380667 | 2 |
| #28380663 | 2 |
| C22⋊Q8×C439 | 2 |
| #468 | 439 |