Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #22579787 | C2 | semidirect |
| 4. #22579787 | C2 | semidirect |
| 5. C2×C4⋊C4×C277 | C2 | semidirect |
| 50. C277 | #397 | semidirect |
| 52. C2×C4⋊C4 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984540 | 2 |
| #22579787 | 2 |
| C2×C4⋊C4×C277 | 2 |
| #397 | 277 |