Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581584 | C2 | semidirect |
| 3. #22581263 | C2 | semidirect |
| 4. #22581252 | C2 | semidirect |
| 5. #22581242 | C2 | semidirect |
| 6. #22581237 | C2 | semidirect |
| 7. #22580993 | C2 | semidirect |
| 8. #22580979 | C2 | semidirect |
| 11. C2×#106×C139 | C2 | semidirect |
| 42. #14555785 | Q8 | semidirect |
| 123. C139 | #3084 | semidirect |
| 132. C2×#106 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581434 | 2 |
| #22581263 | 2 |
| #22581252 | 2 |
| #22581242 | 2 |
| #22581237 | 2 |
| #22580993 | 2 |
| #22580979 | 2 |
| #22580952 | 2 |
| #22580950 | 2 |
| C2×#106×C139 | 2 |
| #3084 | 139 |