Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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. #22581508 | C2 | semidirect |
| 3. #22581309 | C2 | semidirect |
| 4. #22581303 | C2 | semidirect |
| 5. #22581301 | C2 | semidirect |
| 6. #22581300 | C2 | semidirect |
| 7. #22580948 | C2 | semidirect |
| 8. C4×C8×D139 | C2 | semidirect |
| 9. #487×C139 | C2 | semidirect |
| 111. C139 | #3131 | semidirect |
| 117. #487 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581504 | 2 |
| #22581309 | 2 |
| #22581303 | 2 |
| #22581301 | 2 |
| #22581300 | 2 |
| #22580948 | 2 |
| C4×C8×D139 | 2 |
| #487×C139 | 2 |
| #3131 | 139 |