Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22581359 | C2 | semidirect |
| 3. #22581356 | C2 | semidirect |
| 4. #22581349 | C2 | semidirect |
| 31. #14555769 | Q8 | semidirect |
| 60. C139⋊C8 | C2×Q8 | semidirect |
| 92. C139 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581359 | 2 |
| #22581356 | 2 |
| #22581349 | 2 |
| #22580993 | 2 |
| C4×#14555769 | 2 |
| C2×C4⋊Q8×C139 | 2 |
| #3165 | 139 |