Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581688 | C2 | semidirect |
| 2. #22581310 | C2 | semidirect |
| 3. #22581301 | C2 | semidirect |
| 4. #22581250 | C2 | semidirect |
| 5. #22581245 | C2 | semidirect |
| 6. #22581168 | C2 | semidirect |
| 8. Q8×C139⋊C8 | C2 | semidirect |
| 9. C4×#14555773 | C2 | semidirect |
| 10. C4×#14555770 | C2 | semidirect |
| 11. #554×C139 | C2 | semidirect |
| 122. C139 | #3361 | semidirect |
| 125. #554 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581310 | 2 |
| #22581301 | 2 |
| #22581250 | 2 |
| #22581245 | 2 |
| #22581168 | 2 |
| #22581148 | 2 |
| Q8×C139⋊C8 | 2 |
| C4×#14555773 | 2 |
| C4×#14555770 | 2 |
| #554×C139 | 2 |
| #3361 | 139 |