Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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×D2216 | C2 | semidirect |
| 2. C2×#17984548 | C2 | semidirect |
| 3. #22579876 | C2 | semidirect |
| 4. #22579842 | C2 | semidirect |
| 5. #22579809 | C2 | semidirect |
| 6. #22579800 | C2 | semidirect |
| 7. #102×C277 | C2 | semidirect |
| 26. D1108 | D4 | semidirect |
| 53. Dic277 | D8 | semidirect |
| 60. C277 | #459 | semidirect |
| 68. #102 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2216 | 2 |
| C2×#17984548 | 2 |
| #22579876 | 2 |
| #22579842 | 2 |
| #22579809 | 2 |
| #22579800 | 2 |
| #102×C277 | 2 |
| #459 | 277 |