Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22579863 | C2 | direct (N × H) |
| 3. C2×#17984542 | C2 | semidirect |
| 4. C2×C22⋊Dic277 | C2 | semidirect |
| 5. C2×#17984540 | C2 | semidirect |
| 6. C23×C4×C277 | C2 | semidirect |
| 12. #17984542 | C22 | semidirect |
| 13. C22⋊Dic277 | C22 | semidirect |
| 14. #17984540 | C22 | semidirect |
| 18. C22×C4×C277 | C22 | semidirect |
| 47. C2×C277 | #123 | semidirect |
| 51. C277 | C2×#123 | semidirect |
| 54. C23×C4 | D277 | semidirect |
| 67. C22×C4 | C2×D277 | semidirect |
| 100. C2 | #22579863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D277 | 2 |
| #22579863 | 2 |
| C2×#17984542 | 2 |
| C2×C22⋊Dic277 | 2 |
| C2×#17984540 | 2 |
| C23×C4×C277 | 2 |
| C2×#123 | 277 |