Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #22581291 | C2 | semidirect |
| 3. #22581245 | C2 | semidirect |
| 4. #22581240 | C2 | semidirect |
| 5. #22581160 | C2 | semidirect |
| 6. #22581155 | C2 | semidirect |
| 8. #22581058 | C2 | semidirect |
| 9. #22581051 | C2 | semidirect |
| 10. #22581010 | C2 | semidirect |
| 11. #533×C139 | C2 | semidirect |
| 136. C139 | #3116 | semidirect |
| 138. #533 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555785 | 2 |
| #22581291 | 2 |
| #22581245 | 2 |
| #22581240 | 2 |
| #22581160 | 2 |
| #22581155 | 2 |
| #22581113 | 2 |
| #22581058 | 2 |
| #22581051 | 2 |
| #22581010 | 2 |
| #533×C139 | 2 |
| #3116 | 139 |