Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22581332 | C2 | semidirect |
| 5. #22580703 | C2 | semidirect |
| 6. #22580700 | C2 | semidirect |
| 7. #332×C139 | C2 | semidirect |
| 78. C139 | #1689 | semidirect |
| 86. #332 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581332 | 2 |
| #22581234 | 2 |
| #22581230 | 2 |
| #22581030 | 2 |
| #22580703 | 2 |
| #22580700 | 2 |
| #332×C139 | 2 |
| #1689 | 139 |