Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22581501 | C2 | semidirect |
| 2. #22581482 | C2 | semidirect |
| 3. #22581362 | C2 | semidirect |
| 4. #22581317 | C2 | semidirect |
| 5. #22581312 | C2 | semidirect |
| 6. #22581203 | C2 | semidirect |
| 7. #22581196 | C2 | semidirect |
| 8. SD16×Dic139 | C2 | semidirect |
| 9. D8×Dic139 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #496×C139 | C2 | semidirect |
| 110. C8×C139 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 142. #496 | D139 | semidirect |
| 248. C8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581501 | 2 |
| #22581482 | 2 |
| #22581362 | 2 |
| #22581317 | 2 |
| #22581312 | 2 |
| #22581203 | 2 |
| #22581196 | 2 |
| SD16×Dic139 | 2 |
| D8×Dic139 | 2 |
| #22580905 | 2 |
| #496×C139 | 2 |
| #3171 | 139 |