Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic278 | C2 | semidirect |
| 3. #22581303 | C2 | semidirect |
| 5. #22581238 | C2 | semidirect |
| 7. #22581160 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 9. #22581058 | C2 | semidirect |
| 116. C139 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic278 | 2 |
| #22581312 | 2 |
| #22581303 | 2 |
| #22581243 | 2 |
| #22581238 | 2 |
| #22581172 | 2 |
| #22581160 | 2 |
| #22581084 | 2 |
| #22581058 | 2 |
| C4×#14555773 | 2 |
| #556×C139 | 2 |
| #3369 | 139 |