Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581663 | C2 | semidirect |
| 2. #22581317 | C2 | semidirect |
| 3. #22581299 | C2 | semidirect |
| 4. #22581253 | C2 | semidirect |
| 5. #22581243 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581145 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 9. #22581063 | C2 | semidirect |
| 10. C4×#14555770 | C2 | semidirect |
| 11. #550×C139 | C2 | semidirect |
| 77. D556 | #41 | semidirect |
| 129. C139 | #3366 | semidirect |
| 132. #550 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| #22581317 | 2 |
| #22581299 | 2 |
| #22581253 | 2 |
| #22581243 | 2 |
| #22581145 | 2 |
| #22581084 | 2 |
| #22581063 | 2 |
| C4×#14555770 | 2 |
| #550×C139 | 2 |
| #3366 | 139 |