Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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×C22⋊Dic277 | C2 | semidirect |
| 3. #22579794 | C2 | direct (N × H) |
| 4. C2×C22⋊C4×C277 | C2 | semidirect |
| 5. C23×D277 | C4 | semidirect |
| 10. C2×C22⋊D277 | C4 | semidirect |
| 13. C22×Dic277 | C4 | semidirect |
| 15. C22⋊Dic277 | C22 | semidirect |
| 19. C22⋊C4×C277 | C22 | semidirect |
| 23. C22×D277 | C2×C4 | semidirect |
| 32. C2×Dic277 | C2×C4 | semidirect |
| 70. C2×C277 | #99 | semidirect |
| 73. C277 | C2×#99 | semidirect |
| 77. C2×C22⋊C4 | D277 | semidirect |
| 93. C22⋊C4 | C2×D277 | semidirect |
| 145. C2 | #22579794 | 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 |
| C2×C22⋊Dic277 | 2 |
| #22579794 | 2 |
| C2×C22⋊C4×C277 | 2 |
| C2×#99 | 277 |