Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 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. #22581238 | C2 | semidirect |
| 3. #22581084 | C2 | semidirect |
| 4. #22580705 | C2 | semidirect |
| 5. #22580698 | C2 | semidirect |
| 48. C139⋊C8 | SD16 | semidirect |
| 79. C139 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581325 | 2 |
| #22581238 | 2 |
| #22581084 | 2 |
| #22580705 | 2 |
| #22580698 | 2 |
| #22580697 | 2 |
| #460×C139 | 2 |
| #1686 | 139 |