Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#17984833 | C2 | semidirect |
| 3. #22581262 | C2 | semidirect |
| 4. #22581258 | C2 | semidirect |
| 5. #22581255 | C2 | semidirect |
| 6. #22581251 | C2 | semidirect |
| 7. #22580995 | C2 | semidirect |
| 8. #22580993 | C2 | semidirect |
| 9. #22580976 | C2 | semidirect |
| 135. C139 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984833 | 2 |
| #41×Dic139 | 2 |
| #22581262 | 2 |
| #22581258 | 2 |
| #22581255 | 2 |
| #22581251 | 2 |
| #22580995 | 2 |
| #22580993 | 2 |
| #22580976 | 2 |
| #22580954 | 2 |
| #417×C139 | 2 |
| #3080 | 139 |