Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #22581304 | C2 | semidirect |
| 4. #22581289 | C2 | semidirect |
| 5. #22581249 | C2 | semidirect |
| 6. #22581194 | C2 | semidirect |
| 7. #22581164 | C2 | semidirect |
| 8. #22581111 | C2 | semidirect |
| 9. C4×Dic556 | C2 | semidirect |
| 10. C2×#17984767 | C2 | semidirect |
| 93. D4×C139 | Q16 | semidirect |
| 122. C139 | #3299 | semidirect |
| 208. D4 | Dic556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581660 | 2 |
| D4×Dic278 | 2 |
| #22581304 | 2 |
| #22581289 | 2 |
| #22581249 | 2 |
| #22581194 | 2 |
| #22581164 | 2 |
| #22581111 | 2 |
| C4×Dic556 | 2 |
| C2×#17984767 | 2 |
| C8×D4×C139 | 2 |
| #3299 | 139 |