Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #22581678 | C2 | semidirect |
| 3. #22581346 | C2 | semidirect |
| 5. #22581177 | C2 | semidirect |
| 6. #22581157 | C2 | semidirect |
| 8. #22581080 | C2 | semidirect |
| 9. #22581056 | C2 | semidirect |
| 10. C4×#14555775 | C2 | semidirect |
| 11. #462×C139 | C2 | semidirect |
| 121. C139 | #3400 | semidirect |
| 128. #462 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581678 | 2 |
| #22581346 | 2 |
| #22581327 | 2 |
| #22581177 | 2 |
| #22581157 | 2 |
| #22581154 | 2 |
| #22581080 | 2 |
| #22581056 | 2 |
| C4×#14555775 | 2 |
| #462×C139 | 2 |
| #3400 | 139 |