Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22581508 | C2 | semidirect |
| 3. #22581258 | C2 | semidirect |
| 4. #22581252 | C2 | semidirect |
| 5. #22581248 | C2 | semidirect |
| 6. #22581244 | C2 | semidirect |
| 7. #22581230 | C2 | semidirect |
| 8. #22580988 | C2 | semidirect |
| 9. C4⋊C8×D139 | C2 | semidirect |
| 11. #475×C139 | C2 | semidirect |
| 44. #14555786 | Q8 | semidirect |
| 134. C139 | #3076 | semidirect |
| 142. #475 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4×#14555786 | 2 |
| #22581258 | 2 |
| #22581252 | 2 |
| #22581248 | 2 |
| #22581244 | 2 |
| #22581230 | 2 |
| #22580988 | 2 |
| C4⋊C8×D139 | 2 |
| #22580948 | 2 |
| #475×C139 | 2 |
| #3076 | 139 |