Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22580976 | C2 | semidirect |
| 3. C2×#17984770 | C2 | semidirect |
| 4. C2×#17984769 | C2 | semidirect |
| 5. C2×#17984768 | C2 | semidirect |
| 6. C42×Dic139 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 10. #17984840 | C4 | semidirect |
| 11. #17984838 | C4 | semidirect |
| 12. #17984831 | C4 | semidirect |
| 13. #17984829 | C4 | semidirect |
| 49. C4×Dic139 | D4 | semidirect |
| 64. C42×C139 | D4 | semidirect |
| 119. Dic139 | #104 | semidirect |
| 126. C139 | #1962 | semidirect |
| 133. C2×#104 | D139 | semidirect |
| 191. C42 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581499 | 2 |
| #22580976 | 2 |
| C2×#17984770 | 2 |
| C2×#17984769 | 2 |
| C2×#17984768 | 2 |
| C42×Dic139 | 2 |
| C2×#104×C139 | 2 |
| #1962 | 139 |