Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#17984770 | C2 | semidirect |
| 3. C2×#17984769 | C2 | semidirect |
| 4. C2×#17984768 | C2 | semidirect |
| 5. M16×Dic139 | C2 | semidirect |
| 6. C4×Dic139⋊C4 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 10. #17984840 | C4 | semidirect |
| 11. #17984838 | C4 | semidirect |
| 12. #17984831 | C4 | semidirect |
| 13. #17984829 | C4 | semidirect |
| 45. #14555769 | D4 | semidirect |
| 71. M16×C139 | D4 | semidirect |
| 140. Dic139 | #104 | semidirect |
| 148. C139 | #1980 | semidirect |
| 154. C2×#104 | D139 | semidirect |
| 206. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581499 | 2 |
| C2×#17984770 | 2 |
| C2×#17984769 | 2 |
| C2×#17984768 | 2 |
| M16×Dic139 | 2 |
| C4×Dic139⋊C4 | 2 |
| C2×#104×C139 | 2 |
| #1980 | 139 |