Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#17984889 | C2 | semidirect |
| 2. C2×#17984875 | C2 | semidirect |
| 3. C2×#17984862 | C2 | semidirect |
| 4. #22581534 | C2 | semidirect |
| 5. #22581116 | C2 | semidirect |
| 6. #22581110 | C2 | semidirect |
| 7. #22581099 | C2 | semidirect |
| 8. #22581093 | C2 | semidirect |
| 9. C2×#17984765 | C2 | semidirect |
| 10. #22580921 | C2 | semidirect |
| 11. #417×C139 | C2 | semidirect |
| 58. C2×Dic278 | D4 | semidirect |
| 87. #41×C139 | D4 | semidirect |
| 169. C139 | #3013 | semidirect |
| 179. #417 | D139 | semidirect |
| 224. #41 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C2×#17984875 | 2 |
| C2×#17984862 | 2 |
| #22581534 | 2 |
| #22581116 | 2 |
| #22581110 | 2 |
| #22581099 | 2 |
| #22581093 | 2 |
| C2×#17984765 | 2 |
| #22580921 | 2 |
| #417×C139 | 2 |
| #3013 | 139 |