Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 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. #22581508 | C2 | semidirect |
| 3. #22581362 | C2 | semidirect |
| 4. #22581321 | C2 | semidirect |
| 5. #22581312 | C2 | semidirect |
| 6. #22581208 | C2 | semidirect |
| 8. Q16×Dic139 | C2 | semidirect |
| 9. SD16×Dic139 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #497×C139 | C2 | semidirect |
| 129. C139 | #3172 | semidirect |
| 134. #497 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581482 | 2 |
| #22581362 | 2 |
| #22581321 | 2 |
| #22581312 | 2 |
| #22581208 | 2 |
| #22581196 | 2 |
| Q16×Dic139 | 2 |
| SD16×Dic139 | 2 |
| #22580905 | 2 |
| #497×C139 | 2 |
| #3172 | 139 |