Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×#17984553 | C2 | semidirect |
| 3. C2×#17984552 | C2 | semidirect |
| 4. #22579860 | C2 | semidirect |
| 5. #22579800 | C2 | semidirect |
| 6. #22579792 | C2 | semidirect |
| 7. #103×C277 | C2 | semidirect |
| 60. C277 | #452 | semidirect |
| 66. #103 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984564 | 2 |
| C2×#17984553 | 2 |
| C2×#17984552 | 2 |
| #22579860 | 2 |
| #22579800 | 2 |
| #22579792 | 2 |
| #103×C277 | 2 |
| #452 | 277 |