Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22581355 | C2 | semidirect |
| 3. #22581293 | C2 | semidirect |
| 4. #22581287 | C2 | semidirect |
| 5. #22581260 | C2 | semidirect |
| 6. #22581208 | C2 | semidirect |
| 8. #22580994 | C2 | semidirect |
| 9. C4×Q16×C139 | C2 | semidirect |
| 96. C139 | #3352 | semidirect |
| 104. C4×Q16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581644 | 2 |
| #22581355 | 2 |
| #22581293 | 2 |
| #22581287 | 2 |
| #22581260 | 2 |
| #22581208 | 2 |
| #22581032 | 2 |
| #22580994 | 2 |
| C4×Q16×C139 | 2 |
| #3352 | 139 |