Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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. #22579871 | C2 | semidirect |
| 3. #22579802 | C2 | semidirect |
| 4. #22579801 | C2 | semidirect |
| 5. #22579800 | C2 | semidirect |
| 6. #22579790 | C2 | semidirect |
| 7. #102×C277 | C2 | semidirect |
| 52. C277 | #490 | semidirect |
| 59. #102 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579876 | 2 |
| #22579871 | 2 |
| #22579802 | 2 |
| #22579801 | 2 |
| #22579800 | 2 |
| #22579790 | 2 |
| #102×C277 | 2 |
| #490 | 277 |