Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22581753 | C2 | semidirect |
| 2. #22581751 | C2 | semidirect |
| 3. #22580919 | C2 | semidirect |
| 4. C139⋊#338 | C2 | semidirect |
| 5. #408×C139 | C2 | semidirect |
| 92. C139 | #2017 | semidirect |
| 97. #408 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| #22581751 | 2 |
| #22580919 | 2 |
| C139⋊#338 | 2 |
| #408×C139 | 2 |
| #2017 | 139 |