Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581288 | C2 | semidirect |
| 4. #22581260 | C2 | semidirect |
| 5. #22581175 | C2 | semidirect |
| 6. #22581109 | C2 | semidirect |
| 8. #22581058 | C2 | semidirect |
| 9. #22581051 | C2 | semidirect |
| 10. #22581010 | C2 | semidirect |
| 11. C2×C4×Q8×C139 | C2 | semidirect |
| 131. C139 | #3117 | semidirect |
| 134. C2×C4×Q8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581487 | 2 |
| #22581288 | 2 |
| #22581271 | 2 |
| #22581260 | 2 |
| #22581175 | 2 |
| #22581109 | 2 |
| #22581092 | 2 |
| #22581058 | 2 |
| #22581051 | 2 |
| #22581010 | 2 |
| C2×C4×Q8×C139 | 2 |
| #3117 | 139 |