Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17984775 | C2 | semidirect |
| 3. C2×#17984765 | C2 | semidirect |
| 5. C2×#17984753 | C2 | semidirect |
| 6. #22580859 | C2 | semidirect |
| 11. C2×#14555773 | C4 | semidirect |
| 66. C139⋊C8 | C22⋊C4 | semidirect |
| 112. C139 | #1973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555773 | 2 |
| C2×#17984775 | 2 |
| C2×#17984765 | 2 |
| C2×#17984763 | 2 |
| C2×#17984753 | 2 |
| #22580859 | 2 |
| #390×C139 | 2 |
| #1973 | 139 |