Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22580976 | C2 | semidirect |
| 5. C4×Dic139⋊C4 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 7. #339×C139 | C2 | semidirect |
| 10. #17984807 | C4 | semidirect |
| 11. #17984807 | C4 | semidirect |
| 12. #17984804 | C4 | semidirect |
| 13. #17984804 | C4 | semidirect |
| 71. Dic278 | C4⋊C4 | semidirect |
| 73. D556 | C4⋊C4 | semidirect |
| 124. Dic139 | #104 | semidirect |
| 131. C139 | #1806 | semidirect |
| 139. #339 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581421 | 2 |
| #22580976 | 2 |
| C2×#17984770 | 2 |
| C2×#17984768 | 2 |
| C4×Dic139⋊C4 | 2 |
| #22580712 | 2 |
| #339×C139 | 2 |
| #1806 | 139 |