Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22580835 | C2 | semidirect |
| 4. #22580804 | C2 | semidirect |
| 6. C42×Dic139 | C2 | semidirect |
| 7. #383×C139 | C2 | semidirect |
| 9. #17984836 | C4 | semidirect |
| 28. Dic139⋊C4 | C2×C4 | semidirect |
| 37. C42×C139 | C2×C4 | semidirect |
| 68. Dic139 | #126 | semidirect |
| 73. C139 | C4×#126 | semidirect |
| 78. #383 | D139 | semidirect |
| 111. C42 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984836 | 2 |
| #22580842 | 2 |
| #22580835 | 2 |
| #22580804 | 2 |
| #22580800 | 2 |
| C42×Dic139 | 2 |
| #383×C139 | 2 |
| C4×#126 | 139 |