Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #22581660 | C2 | semidirect |
| 2. #22581623 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581299 | C2 | semidirect |
| 5. #22581255 | C2 | semidirect |
| 6. #22581244 | C2 | semidirect |
| 7. #22581146 | C2 | semidirect |
| 8. #22581080 | C2 | semidirect |
| 9. #22581065 | C2 | semidirect |
| 10. C4×#14555770 | C2 | semidirect |
| 11. #459×C139 | C2 | semidirect |
| 97. D4×C139 | #41 | semidirect |
| 129. C139 | #3366 | semidirect |
| 138. #459 | D139 | semidirect |
| 218. D4 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581660 | 2 |
| #22581623 | 2 |
| #22581316 | 2 |
| #22581299 | 2 |
| #22581255 | 2 |
| #22581244 | 2 |
| #22581146 | 2 |
| #22581080 | 2 |
| #22581065 | 2 |
| C4×#14555770 | 2 |
| #459×C139 | 2 |
| #3366 | 139 |