Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #22580820 | C2 | semidirect |
| 3. #22580819 | C2 | semidirect |
| 6. C4⋊C4×Dic139 | C2 | semidirect |
| 8. #22580798 | C2 | semidirect |
| 9. #382×C139 | C2 | semidirect |
| 19. C42×D139 | C4 | semidirect |
| 105. C139 | #2283 | semidirect |
| 110. #382 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D139 | 2 |
| #22580820 | 2 |
| #22580819 | 2 |
| #22580815 | 2 |
| #22580810 | 2 |
| C4⋊C4×Dic139 | 2 |
| #22580800 | 2 |
| #22580798 | 2 |
| #382×C139 | 2 |
| #2283 | 139 |