Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#17984548 | C2 | semidirect |
| 2. #22579876 | C2 | semidirect |
| 3. D4×Dic277 | C2 | semidirect |
| 4. #22579809 | C2 | semidirect |
| 5. #22579802 | C2 | semidirect |
| 6. #22579801 | C2 | semidirect |
| 7. C2×D8×C277 | C2 | semidirect |
| 36. D4×C277 | D4 | semidirect |
| 53. Dic277 | D8 | semidirect |
| 60. C277 | #459 | semidirect |
| 63. C2×D8 | D277 | semidirect |
| 92. D4 | C22⋊D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984548 | 2 |
| #22579876 | 2 |
| D4×Dic277 | 2 |
| #22579809 | 2 |
| #22579802 | 2 |
| #22579801 | 2 |
| C2×D8×C277 | 2 |
| #459 | 277 |