Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14555774 | C2 | semidirect |
| 3. C22×D1112 | C2 | semidirect |
| 4. C2×#17984816 | C2 | semidirect |
| 5. #22581100 | C2 | direct (N × H) |
| 6. C2×#17984767 | C2 | semidirect |
| 7. C2×#17984764 | C2 | semidirect |
| 8. C2×C22⋊C8×C139 | C2 | semidirect |
| 12. C2×#14555785 | C22 | semidirect |
| 20. C2×#14555774 | C22 | semidirect |
| 22. C2×D1112 | C22 | semidirect |
| 24. #17984816 | C22 | semidirect |
| 27. #17984767 | C22 | semidirect |
| 28. #17984764 | C22 | semidirect |
| 32. C22⋊C8×C139 | C22 | semidirect |
| 40. C2×Dic278 | D4 | semidirect |
| 47. C2×D556 | D4 | semidirect |
| 84. Dic278 | C2×D4 | semidirect |
| 90. D556 | C2×D4 | semidirect |
| 137. C2×C139 | #449 | semidirect |
| 143. C139 | C2×#449 | semidirect |
| 152. C2×C22⋊C8 | D139 | semidirect |
| 176. C22⋊C8 | C2×D139 | semidirect |
| 283. C2 | #22581100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555785 | 2 |
| C22×#14555774 | 2 |
| C22×D1112 | 2 |
| C2×#17984816 | 2 |
| #22581100 | 2 |
| C2×#17984767 | 2 |
| C2×#17984764 | 2 |
| C2×C22⋊C8×C139 | 2 |
| C2×#449 | 139 |