Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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×#17984777 | C2 | semidirect |
| 3. C2×#17984770 | C2 | semidirect |
| 4. #22580921 | C2 | semidirect |
| 5. #22580920 | C2 | semidirect |
| 6. C2×C4×C139⋊C8 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 12. C2×#14555773 | C4 | semidirect |
| 13. C2×#14555772 | C4 | semidirect |
| 14. C2×#14555770 | C4 | semidirect |
| 119. C139 | #1974 | semidirect |
| 124. C2×#104 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984862 | 2 |
| C2×#17984777 | 2 |
| C2×#17984770 | 2 |
| #22580921 | 2 |
| #22580920 | 2 |
| C2×C4×C139⋊C8 | 2 |
| C2×#104×C139 | 2 |
| #1974 | 139 |