Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 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. #22581689 | C2 | semidirect |
| 2. #22581624 | C2 | semidirect |
| 3. #22581341 | C2 | semidirect |
| 4. #22581329 | C2 | semidirect |
| 5. #22581167 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581146 | C2 | semidirect |
| 8. #22581080 | C2 | semidirect |
| 9. #22581062 | C2 | semidirect |
| 10. C4×#14555773 | C2 | semidirect |
| 11. #459×C139 | C2 | semidirect |
| 94. C139⋊C8 | #41 | semidirect |
| 134. C139 | #3399 | semidirect |
| 143. #459 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581689 | 2 |
| #22581624 | 2 |
| #22581341 | 2 |
| #22581329 | 2 |
| #22581167 | 2 |
| #22581154 | 2 |
| #22581146 | 2 |
| #22581080 | 2 |
| #22581062 | 2 |
| C4×#14555773 | 2 |
| #459×C139 | 2 |
| #3399 | 139 |