Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. D4×Dic278 | C2 | semidirect |
| 2. #22581305 | C2 | semidirect |
| 3. #22581283 | C2 | semidirect |
| 4. #22581235 | C2 | semidirect |
| 5. #22581180 | C2 | semidirect |
| 6. #22581158 | C2 | semidirect |
| 7. #22581091 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. C2×#17984765 | C2 | semidirect |
| 81. Dic278 | #41 | semidirect |
| 95. D4×C139 | SD16 | semidirect |
| 128. C139 | #3298 | semidirect |
| 217. D4 | #14555773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic278 | 2 |
| #22581305 | 2 |
| #22581283 | 2 |
| #22581235 | 2 |
| #22581180 | 2 |
| #22581158 | 2 |
| #22581091 | 2 |
| C4×#14555773 | 2 |
| D4×C139⋊C8 | 2 |
| C2×#17984765 | 2 |
| #547×C139 | 2 |
| #3298 | 139 |