Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D556 | C2 | semidirect |
| 3. #22581305 | C2 | semidirect |
| 4. #22581285 | C2 | semidirect |
| 5. #22581183 | C2 | semidirect |
| 6. #22581159 | C2 | semidirect |
| 7. #22581093 | C2 | semidirect |
| 8. C4×#14555772 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #103×D139 | C2 | semidirect |
| 11. #475×C139 | C2 | semidirect |
| 85. D556 | SD16 | semidirect |
| 98. Q8×C139 | #41 | semidirect |
| 128. C139 | #3298 | semidirect |
| 134. #475 | D139 | semidirect |
| 213. Q8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D556 | 2 |
| #22581606 | 2 |
| #22581305 | 2 |
| #22581285 | 2 |
| #22581183 | 2 |
| #22581159 | 2 |
| #22581093 | 2 |
| C4×#14555772 | 2 |
| #22581018 | 2 |
| #103×D139 | 2 |
| #475×C139 | 2 |
| #3298 | 139 |