Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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. #22581719 | C2 | semidirect |
| 3. #22580937 | C2 | semidirect |
| 4. #22580934 | C2 | semidirect |
| 5. C2×#17984760 | C2 | semidirect |
| 6. #101×D139 | C2 | semidirect |
| 7. #413×C139 | C2 | semidirect |
| 114. C139 | #2889 | semidirect |
| 120. #413 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| #22581719 | 2 |
| #22580937 | 2 |
| #22580934 | 2 |
| C2×#17984760 | 2 |
| #101×D139 | 2 |
| #413×C139 | 2 |
| #2889 | 139 |