Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 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. #22581508 | C2 | semidirect |
| 3. #22581347 | C2 | semidirect |
| 4. #22581323 | C2 | semidirect |
| 5. #22581315 | C2 | semidirect |
| 6. #22581212 | C2 | semidirect |
| 8. #22581047 | C2 | semidirect |
| 9. #22581040 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #501×C139 | C2 | semidirect |
| 129. C139 | #3172 | semidirect |
| 133. #501 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581488 | 2 |
| #22581347 | 2 |
| #22581323 | 2 |
| #22581315 | 2 |
| #22581212 | 2 |
| #22581200 | 2 |
| #22581047 | 2 |
| #22581040 | 2 |
| #22580905 | 2 |
| #501×C139 | 2 |
| #3172 | 139 |