Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22581719 | C2 | semidirect |
| 3. #22580947 | C2 | semidirect |
| 4. #22580920 | C2 | semidirect |
| 5. #22580723 | C2 | semidirect |
| 6. #22580717 | C2 | semidirect |
| 7. #421×C139 | C2 | semidirect |
| 9. #17984873 | C4 | semidirect |
| 11. #17984868 | C4 | semidirect |
| 118. C139 | #1881 | semidirect |
| 122. #421 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581751 | 2 |
| #22581719 | 2 |
| #22580947 | 2 |
| #22580920 | 2 |
| #22580723 | 2 |
| #22580717 | 2 |
| #421×C139 | 2 |
| #1881 | 139 |