Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22581504 | C2 | semidirect |
| 2. #22581488 | C2 | semidirect |
| 3. #22581342 | C2 | semidirect |
| 4. #22581319 | C2 | semidirect |
| 5. #22581315 | C2 | semidirect |
| 6. #22581207 | C2 | semidirect |
| 7. #22581200 | C2 | semidirect |
| 8. #22581040 | C2 | semidirect |
| 9. #22581035 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #501×C139 | C2 | semidirect |
| 110. C8×C139 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 141. #501 | D139 | semidirect |
| 248. C8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581504 | 2 |
| #22581488 | 2 |
| #22581342 | 2 |
| #22581319 | 2 |
| #22581315 | 2 |
| #22581207 | 2 |
| #22581200 | 2 |
| #22581040 | 2 |
| #22581035 | 2 |
| #22580905 | 2 |
| #501×C139 | 2 |
| #3171 | 139 |