Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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. C2×#17984798 | C2 | semidirect |
| 3. #22580816 | C2 | semidirect |
| 4. #22580812 | C2 | semidirect |
| 6. #22580800 | C2 | semidirect |
| 7. #381×C139 | C2 | semidirect |
| 11. C22×C4×D139 | C4 | semidirect |
| 15. C2×Dic139⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic139 | C22 | semidirect |
| 19. C139⋊#95 | C22 | semidirect |
| 22. #95×C139 | C22 | semidirect |
| 56. C2×Dic139 | C22⋊C4 | semidirect |
| 82. C2×D139 | #117 | semidirect |
| 93. C139 | #2280 | semidirect |
| 98. #381 | D139 | semidirect |
| 116. #95 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D139 | 2 |
| C2×#17984798 | 2 |
| #22580816 | 2 |
| #22580812 | 2 |
| #22580808 | 2 |
| #22580800 | 2 |
| #381×C139 | 2 |
| #2280 | 139 |