Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22581556 | C2 | semidirect |
| 2. #22581255 | C2 | semidirect |
| 3. #22581252 | C2 | semidirect |
| 4. #22581206 | C2 | semidirect |
| 5. #22581187 | C2 | semidirect |
| 6. #22581147 | C2 | semidirect |
| 7. #22581146 | C2 | semidirect |
| 8. #22580981 | C2 | semidirect |
| 9. #469×C139 | C2 | semidirect |
| 109. C139 | #3259 | semidirect |
| 115. #469 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581556 | 2 |
| #22581255 | 2 |
| #22581252 | 2 |
| #22581206 | 2 |
| #22581187 | 2 |
| #22581147 | 2 |
| #22581146 | 2 |
| #22580981 | 2 |
| #469×C139 | 2 |
| #3259 | 139 |