Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #22581676 | C2 | semidirect |
| 3. #22581300 | C2 | semidirect |
| 4. #22581280 | C2 | semidirect |
| 5. #22581238 | C2 | semidirect |
| 6. #22581185 | C2 | semidirect |
| 7. #22581153 | C2 | semidirect |
| 8. #22581114 | C2 | semidirect |
| 9. C8×D556 | C2 | semidirect |
| 10. #22580948 | C2 | semidirect |
| 11. C4×Q16×C139 | C2 | semidirect |
| 127. C139 | #3304 | semidirect |
| 137. C4×Q16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581625 | 2 |
| #22581300 | 2 |
| #22581280 | 2 |
| #22581238 | 2 |
| #22581185 | 2 |
| #22581153 | 2 |
| #22581114 | 2 |
| C8×D556 | 2 |
| #22580948 | 2 |
| C4×Q16×C139 | 2 |
| #3304 | 139 |