Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×Q8×Dic139 | C2 | semidirect |
| 5. #22580842 | C2 | semidirect |
| 6. #22580827 | C2 | semidirect |
| 7. #22580822 | C2 | semidirect |
| 8. #22580799 | C2 | semidirect |
| 9. #391×C139 | C2 | semidirect |
| 12. #17984831 | C4 | semidirect |
| 45. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 47. C4×Dic139 | C2×C4 | semidirect |
| 51. C2×Q8×C139 | C2×C4 | semidirect |
| 111. C139 | #2326 | semidirect |
| 116. #391 | D139 | semidirect |
| 145. C2×Q8 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984831 | 2 |
| C2×Q8×Dic139 | 2 |
| C2×#17984804 | 2 |
| #22580855 | 2 |
| #22580842 | 2 |
| #22580827 | 2 |
| #22580822 | 2 |
| #22580799 | 2 |
| #391×C139 | 2 |
| #2326 | 139 |