Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic278 | C2 | semidirect |
| 3. #22580858 | C2 | semidirect |
| 5. #22580841 | C2 | semidirect |
| 6. #22580826 | C2 | semidirect |
| 7. #22580822 | C2 | semidirect |
| 8. #22580799 | C2 | semidirect |
| 11. #17984829 | C4 | semidirect |
| 32. C2×Dic278 | C2×C4 | semidirect |
| 41. C22⋊Dic139 | C2×C4 | semidirect |
| 44. C4×Dic139 | C2×C4 | semidirect |
| 111. C139 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984829 | 2 |
| C2×C4×Dic278 | 2 |
| #22580858 | 2 |
| #22580856 | 2 |
| #22580841 | 2 |
| #22580826 | 2 |
| #22580822 | 2 |
| #22580799 | 2 |
| C2×C4×D4×C139 | 2 |
| #2326 | 139 |