Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22581333 | C2 | semidirect |
| 3. #22581244 | C2 | semidirect |
| 4. #22581243 | C2 | semidirect |
| 5. #22580701 | C2 | semidirect |
| 6. #22580682 | C2 | semidirect |
| 7. D4⋊C8×C139 | C2 | semidirect |
| 92. C139 | #1634 | semidirect |
| 100. D4⋊C8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581333 | 2 |
| #22581244 | 2 |
| #22581243 | 2 |
| #22580701 | 2 |
| #22580682 | 2 |
| D4⋊C8×C139 | 2 |
| #1634 | 139 |