Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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×#17984799 | C2 | semidirect |
| 4. #22580849 | C2 | semidirect |
| 5. #22580842 | C2 | semidirect |
| 6. C4×(C2×D139)⋊C4 | C2 | semidirect |
| 7. C42×Dic139 | C2 | semidirect |
| 8. C4×C4⋊C4×C139 | C2 | semidirect |
| 11. C4×D556 | C4 | semidirect |
| 44. C4×Dic139 | D4 | semidirect |
| 91. C4×C139 | #117 | semidirect |
| 102. C139 | #2293 | semidirect |
| 109. C4×C4⋊C4 | D139 | semidirect |
| 197. C4 | #17984799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D556 | 2 |
| C2×#17984799 | 2 |
| #22580854 | 2 |
| #22580849 | 2 |
| #22580842 | 2 |
| C4×(C2×D139)⋊C4 | 2 |
| C42×Dic139 | 2 |
| C4×C4⋊C4×C139 | 2 |
| #2293 | 139 |