Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C4⋊C4×Dic139 | C2 | semidirect |
| 4. C4×(C2×D139)⋊C4 | C2 | semidirect |
| 5. #22580800 | C2 | semidirect |
| 6. #22580799 | C2 | semidirect |
| 7. #95×D139 | C2 | semidirect |
| 8. C4×C4⋊C4×C139 | C2 | semidirect |
| 12. C4×D556 | C4 | semidirect |
| 13. #17984804 | C4 | semidirect |
| 36. C2×C4×D139 | C2×C4 | semidirect |
| 37. C2×C4×D139 | C2×C4 | semidirect |
| 38. C4⋊Dic139 | C2×C4 | semidirect |
| 39. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 40. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 42. C4×Dic139 | C2×C4 | semidirect |
| 47. C4⋊C4×C139 | C2×C4 | semidirect |
| 49. C42×C139 | C2×C4 | semidirect |
| 55. D556 | C42 | semidirect |
| 100. C139 | #2275 | semidirect |
| 105. C4×C4⋊C4 | D139 | semidirect |
| 144. C4⋊C4 | C4×D139 | semidirect |
| 150. C42 | C4×D139 | 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×#17984804 | 2 |
| C4⋊C4×Dic139 | 2 |
| C4×(C2×D139)⋊C4 | 2 |
| #22580800 | 2 |
| #22580799 | 2 |
| #95×D139 | 2 |
| C4×C4⋊C4×C139 | 2 |
| #2275 | 139 |