Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14555773 | C2 | semidirect |
| 2. C23×C139⋊C8 | C2 | semidirect |
| 3. C2×#17984821 | C2 | semidirect |
| 4. #22581180 | C2 | direct (N × H) |
| 5. C2×#17984773 | C2 | semidirect |
| 6. C2×#17984765 | C2 | semidirect |
| 7. C2×#17984763 | C2 | semidirect |
| 11. C2×#14555773 | C22 | semidirect |
| 15. C22×C139⋊C8 | C22 | semidirect |
| 17. #17984821 | C22 | semidirect |
| 21. #17984773 | C22 | semidirect |
| 22. #17984765 | C22 | semidirect |
| 23. #17984763 | C22 | semidirect |
| 40. C2×C139⋊C8 | D4 | semidirect |
| 73. C139⋊C8 | C2×D4 | semidirect |
| 80. C23×C139 | SD16 | semidirect |
| 107. C22×C139 | C2×SD16 | semidirect |
| 119. C2×C139 | #465 | semidirect |
| 123. C139 | C2×#465 | semidirect |
| 195. C23 | #14555773 | semidirect |
| 231. C22 | C2×#14555773 | semidirect |
| 243. C2 | #22581180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555773 | 2 |
| C23×C139⋊C8 | 2 |
| C2×#17984821 | 2 |
| #22581180 | 2 |
| C2×#17984773 | 2 |
| C2×#17984765 | 2 |
| C2×#17984763 | 2 |
| C2×#121×C139 | 2 |
| C2×#465 | 139 |