Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14555774 | C2 | semidirect |
| 2. C22×#14555773 | C2 | semidirect |
| 4. C2×#17984807 | C2 | semidirect |
| 5. #22581152 | C2 | direct (N × H) |
| 6. C2×Dic139⋊C8 | C2 | semidirect |
| 7. C2×#17984762 | C2 | semidirect |
| 8. C2×#102×C139 | C2 | semidirect |
| 14. C2×#14555774 | C22 | semidirect |
| 16. C2×#14555773 | C22 | semidirect |
| 21. #17984807 | C22 | semidirect |
| 25. Dic139⋊C8 | C22 | semidirect |
| 26. #17984762 | C22 | semidirect |
| 30. #102×C139 | C22 | semidirect |
| 34. C2×Dic278 | D4 | semidirect |
| 72. Dic278 | C2×D4 | semidirect |
| 81. C2×Dic139 | SD16 | semidirect |
| 118. Dic139 | C2×SD16 | semidirect |
| 120. C2×C139 | #460 | semidirect |
| 125. C139 | C2×#460 | semidirect |
| 134. C2×#102 | D139 | semidirect |
| 156. #102 | C2×D139 | semidirect |
| 247. C2 | #22581152 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555774 | 2 |
| C22×#14555773 | 2 |
| C2×#17984838 | 2 |
| C2×#17984807 | 2 |
| #22581152 | 2 |
| C2×Dic139⋊C8 | 2 |
| C2×#17984762 | 2 |
| C2×#102×C139 | 2 |
| C2×#460 | 139 |