Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22580848 | C2 | semidirect |
| 3. #22580847 | C2 | semidirect |
| 4. #22580841 | C2 | semidirect |
| 5. #22580837 | C2 | semidirect |
| 7. #22580825 | C2 | semidirect |
| 8. #22580811 | C2 | semidirect |
| 12. #17984823 | C4 | semidirect |
| 36. C22×Dic139 | C2×C4 | semidirect |
| 44. Dic139⋊C4 | C2×C4 | semidirect |
| 48. C22⋊Dic139 | C2×C4 | semidirect |
| 126. C139 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984823 | 2 |
| #22580848 | 2 |
| #22580847 | 2 |
| #22580841 | 2 |
| #22580837 | 2 |
| #22580833 | 2 |
| #22580825 | 2 |
| #22580811 | 2 |
| #390×C139 | 2 |
| #2376 | 139 |