Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22581007 | C2 | semidirect |
| 3. #22581003 | C2 | semidirect |
| 4. #22580679 | C2 | semidirect |
| 7. #324×C139 | C2 | semidirect |
| 106. C139 | #1473 | semidirect |
| 112. #324 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984837 | 2 |
| #22581007 | 2 |
| #22581003 | 2 |
| #22580679 | 2 |
| #22580676 | 2 |
| #324×C139 | 2 |
| #1473 | 139 |