Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #22581297 | C2 | semidirect |
| 4. #22581285 | C2 | semidirect |
| 5. #22581245 | C2 | semidirect |
| 6. #22581235 | C2 | semidirect |
| 7. #22581212 | C2 | semidirect |
| 8. C4×Dic556 | C2 | semidirect |
| 10. #22580992 | C2 | semidirect |
| 11. #498×C139 | C2 | semidirect |
| 116. C139 | #3356 | semidirect |
| 120. #498 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581677 | 2 |
| #22581664 | 2 |
| #22581297 | 2 |
| #22581285 | 2 |
| #22581245 | 2 |
| #22581235 | 2 |
| #22581212 | 2 |
| C4×Dic556 | 2 |
| #22581032 | 2 |
| #22580992 | 2 |
| #498×C139 | 2 |
| #3356 | 139 |