Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 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×#17984766 | C2 | semidirect |
| 5. C2×C8×Dic139 | C2 | semidirect |
| 6. #22580818 | C2 | semidirect |
| 7. C2×#103×C139 | C2 | semidirect |
| 11. #17984831 | C4 | semidirect |
| 111. C139 | #1958 | semidirect |
| 115. C2×#103 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984831 | 2 |
| C2×#17984766 | 2 |
| C2×#17984764 | 2 |
| C2×#17984762 | 2 |
| C2×C8×Dic139 | 2 |
| #22580818 | 2 |
| C2×#103×C139 | 2 |
| #1958 | 139 |