Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581676 | C2 | semidirect |
| 3. #22581356 | C2 | semidirect |
| 4. #22581287 | C2 | semidirect |
| 5. #22581279 | C2 | semidirect |
| 6. #22581234 | C2 | semidirect |
| 7. #22581202 | C2 | semidirect |
| 8. C4×#14555772 | C2 | semidirect |
| 9. #22581030 | C2 | semidirect |
| 10. #22580992 | C2 | semidirect |
| 11. #475×C139 | C2 | semidirect |
| 89. C139⋊C8 | #41 | semidirect |
| 122. C139 | #3353 | semidirect |
| 129. #475 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581606 | 2 |
| #22581356 | 2 |
| #22581287 | 2 |
| #22581279 | 2 |
| #22581234 | 2 |
| #22581202 | 2 |
| C4×#14555772 | 2 |
| #22581030 | 2 |
| #22580992 | 2 |
| #475×C139 | 2 |
| #3353 | 139 |