Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984889 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C2×#17984867 | C2 | semidirect |
| 4. C2×#17984830 | C2 | semidirect |
| 5. #22581127 | C2 | direct (N × H) |
| 6. C2×#17984770 | C2 | semidirect |
| 7. C2×#17984760 | C2 | semidirect |
| 8. C2×#104×C139 | C2 | semidirect |
| 12. #17984889 | C22 | semidirect |
| 22. #17984870 | C22 | semidirect |
| 24. #17984867 | C22 | semidirect |
| 31. #17984830 | C22 | semidirect |
| 33. #17984770 | C22 | semidirect |
| 34. #17984760 | C22 | semidirect |
| 38. #104×C139 | C22 | semidirect |
| 171. C2×C139 | #454 | semidirect |
| 175. C139 | C2×#454 | semidirect |
| 183. C2×#104 | D139 | semidirect |
| 213. #104 | C2×D139 | semidirect |
| 349. C2 | #22581127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C2×#17984870 | 2 |
| C2×#17984867 | 2 |
| C2×#17984830 | 2 |
| #22581127 | 2 |
| C2×#17984770 | 2 |
| C2×#17984760 | 2 |
| C2×#104×C139 | 2 |
| C2×#454 | 139 |