Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 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×#14555768 | C2 | semidirect |
| 3. C2×#17984822 | C2 | semidirect |
| 5. #22581200 | C2 | direct (N × H) |
| 6. C2×#17984765 | C2 | semidirect |
| 7. C2×#17984762 | C2 | semidirect |
| 8. C2×#107×C139 | C2 | semidirect |
| 14. C2×#14555774 | C22 | semidirect |
| 16. C2×#14555768 | C22 | semidirect |
| 19. #17984822 | C22 | semidirect |
| 25. #17984765 | C22 | semidirect |
| 26. #17984762 | C22 | semidirect |
| 30. #107×C139 | C22 | semidirect |
| 59. C2×C8×C139 | D4 | semidirect |
| 97. C8×C139 | C2×D4 | semidirect |
| 117. C2×C139 | #468 | semidirect |
| 123. C139 | C2×#468 | semidirect |
| 130. C2×#107 | D139 | semidirect |
| 152. #107 | C2×D139 | semidirect |
| 180. C2×C8 | D556 | semidirect |
| 221. C8 | C2×D556 | semidirect |
| 243. C2 | #22581200 | 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×#14555768 | 2 |
| C2×#17984822 | 2 |
| C2×#17984817 | 2 |
| #22581200 | 2 |
| C2×#17984765 | 2 |
| C2×#17984762 | 2 |
| C2×#107×C139 | 2 |
| C2×#468 | 139 |