Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22579875 | C2 | semidirect |
| 2. #22579871 | C2 | semidirect |
| 3. #22579870 | C2 | semidirect |
| 5. #22579860 | C2 | semidirect |
| 6. #22579859 | C2 | semidirect |
| 7. #22579845 | C2 | semidirect |
| 9. #22579839 | C2 | semidirect |
| 10. #22579838 | C2 | semidirect |
| 11. C2×C4⋊C4×C277 | C2 | semidirect |
| 72. C277 | #552 | semidirect |
| 84. C2×C4⋊C4 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579875 | 2 |
| #22579871 | 2 |
| #22579870 | 2 |
| #22579863 | 2 |
| #22579860 | 2 |
| #22579859 | 2 |
| #22579845 | 2 |
| C4×C22⋊D277 | 2 |
| #22579839 | 2 |
| #22579838 | 2 |
| C2×C4⋊C4×C277 | 2 |
| #552 | 277 |