Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14555785 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C2×#17984816 | C2 | semidirect |
| 4. #22581100 | C2 | semidirect |
| 5. #22581094 | C2 | semidirect |
| 6. #22581089 | C2 | semidirect |
| 7. #22580955 | C2 | semidirect |
| 8. #407×C139 | C2 | semidirect |
| 13. C2×#14555785 | C22 | semidirect |
| 14. C22×Dic278 | C22 | semidirect |
| 15. C22×D556 | C22 | semidirect |
| 16. C22×D556 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 22. C2×D1112 | C22 | semidirect |
| 26. #17984816 | C22 | semidirect |
| 27. C2×C4⋊Dic139 | C22 | semidirect |
| 29. #17984767 | C22 | semidirect |
| 30. #17984764 | C22 | semidirect |
| 32. C2×M16×C139 | C22 | semidirect |
| 33. C22⋊C8×C139 | C22 | semidirect |
| 34. C22⋊C8×C139 | C22 | semidirect |
| 42. #14555785 | D4 | semidirect |
| 89. Dic278 | C2×D4 | semidirect |
| 94. D556 | C2×D4 | semidirect |
| 131. C22×C139 | AGL(1,ℤ/8) | semidirect |
| 155. C139 | #3006 | semidirect |
| 164. #407 | D139 | semidirect |
| 180. C2×M16 | C2×D139 | semidirect |
| 189. C22⋊C8 | C2×D139 | semidirect |
| 190. C22⋊C8 | C2×D139 | semidirect |
| 295. C22 | #17984870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555785 | 2 |
| C2×#17984870 | 2 |
| C2×#17984816 | 2 |
| #22581100 | 2 |
| #22581094 | 2 |
| #22581089 | 2 |
| #22580955 | 2 |
| #407×C139 | 2 |
| #3006 | 139 |