Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22579875 | C2 | semidirect |
| 2. #22579871 | C2 | semidirect |
| 3. #22579865 | C2 | semidirect |
| 4. #22579864 | C2 | semidirect |
| 5. #22579856 | C2 | semidirect |
| 7. #22579840 | C2 | semidirect |
| 8. C2×#17984542 | C2 | semidirect |
| 9. C22⋊Q8×C277 | C2 | semidirect |
| 66. C277 | #539 | semidirect |
| 73. C22⋊Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579875 | 2 |
| #22579871 | 2 |
| #22579865 | 2 |
| #22579864 | 2 |
| #22579856 | 2 |
| #22579854 | 2 |
| #22579840 | 2 |
| C2×#17984542 | 2 |
| C22⋊Q8×C277 | 2 |
| #539 | 277 |