Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #22581363 | C2 | semidirect |
| 4. #22581362 | C2 | semidirect |
| 5. #22581361 | C2 | semidirect |
| 6. #22581360 | C2 | semidirect |
| 7. #22581359 | C2 | semidirect |
| 11. #501×C139 | C2 | semidirect |
| 50. C8×D139 | Q8 | semidirect |
| 121. C139 | #3162 | semidirect |
| 130. #501 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581509 | 2 |
| #22581508 | 2 |
| #22581363 | 2 |
| #22581362 | 2 |
| #22581361 | 2 |
| #22581360 | 2 |
| #22581359 | 2 |
| #22580990 | 2 |
| #22580988 | 2 |
| #97×D139 | 2 |
| #501×C139 | 2 |
| #3162 | 139 |