Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #22581510 | C2 | semidirect |
| 2. #22581363 | C2 | semidirect |
| 3. #22581348 | C2 | semidirect |
| 4. #22581323 | C2 | semidirect |
| 5. #22581312 | C2 | semidirect |
| 6. #22581209 | C2 | semidirect |
| 8. C4×#14555775 | C2 | semidirect |
| 9. C4×#14555773 | C2 | semidirect |
| 10. C4×#14555769 | C2 | semidirect |
| 129. C139 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581363 | 2 |
| #22581348 | 2 |
| #22581323 | 2 |
| #22581312 | 2 |
| #22581209 | 2 |
| #22581197 | 2 |
| C4×#14555775 | 2 |
| C4×#14555773 | 2 |
| C4×#14555769 | 2 |
| #529×C139 | 2 |
| #3172 | 139 |