Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581681 | C2 | semidirect |
| 3. #22581346 | C2 | semidirect |
| 5. #22581178 | C2 | semidirect |
| 6. #22581163 | C2 | semidirect |
| 7. #22581157 | C2 | semidirect |
| 9. #22581083 | C2 | semidirect |
| 10. #22581052 | C2 | semidirect |
| 11. C4×Q16×C139 | C2 | semidirect |
| 121. C139 | #3400 | semidirect |
| 133. C4×Q16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581681 | 2 |
| #22581346 | 2 |
| #22581326 | 2 |
| #22581178 | 2 |
| #22581163 | 2 |
| #22581157 | 2 |
| #22581153 | 2 |
| #22581083 | 2 |
| #22581052 | 2 |
| C4×Q16×C139 | 2 |
| #3400 | 139 |