Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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×#17984801 | C2 | semidirect |
| 2. #22580816 | C2 | semidirect |
| 3. #22580813 | C2 | semidirect |
| 5. C4×C22⋊Dic139 | C2 | semidirect |
| 8. C2×C4⋊Dic139 | C22 | semidirect |
| 11. C2×C4×Dic139 | C22 | semidirect |
| 12. C139⋊#95 | C22 | semidirect |
| 15. C23×C4×C139 | C4 | semidirect |
| 59. C2×C4×C139 | C22⋊C4 | semidirect |
| 72. C22×C139 | #117 | semidirect |
| 85. C139 | #2280 | semidirect |
| 95. C23×C4 | Dic139 | semidirect |
| 145. C2×C4 | C22⋊Dic139 | semidirect |
| 158. C22 | #17984801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984801 | 2 |
| #22580816 | 2 |
| #22580813 | 2 |
| #22580809 | 2 |
| C4×C22⋊Dic139 | 2 |
| C24×C4×C139 | 2 |
| #2280 | 139 |