Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581323 | C2 | semidirect |
| 3. #22581315 | C2 | semidirect |
| 4. #22581310 | C2 | semidirect |
| 5. #22581305 | C2 | semidirect |
| 6. #22580961 | C2 | semidirect |
| 9. C2×#17984765 | C2 | semidirect |
| 10. #22580909 | C2 | semidirect |
| 11. #544×C139 | C2 | semidirect |
| 127. C139 | #3137 | semidirect |
| 129. #544 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581529 | 2 |
| #22581323 | 2 |
| #22581315 | 2 |
| #22581310 | 2 |
| #22581305 | 2 |
| #22580961 | 2 |
| #22580952 | 2 |
| #22580947 | 2 |
| C2×#17984765 | 2 |
| #22580909 | 2 |
| #544×C139 | 2 |
| #3137 | 139 |