Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×Dic554 | C2 | semidirect |
| 4. #22579814 | C2 | semidirect |
| 5. #22579805 | C2 | semidirect |
| 7. #97×C277 | C2 | semidirect |
| 11. #17984552 | C4 | semidirect |
| 22. Dic554 | C2×C4 | semidirect |
| 33. C8×C277 | C2×C4 | semidirect |
| 49. C277 | #440 | semidirect |
| 57. #97 | D277 | semidirect |
| 83. C8 | C4×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984552 | 2 |
| C4×Dic554 | 2 |
| C4×D1108 | 2 |
| #22579814 | 2 |
| #22579805 | 2 |
| #22579802 | 2 |
| #97×C277 | 2 |
| #440 | 277 |