Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#17984872 | C2 | semidirect |
| 2. C2×#17984821 | C2 | semidirect |
| 3. #22581115 | C2 | semidirect |
| 4. #22581109 | C2 | semidirect |
| 5. #22581104 | C2 | semidirect |
| 6. #22580954 | C2 | semidirect |
| 7. #22580917 | C2 | semidirect |
| 9. C22×Dic278 | C22 | semidirect |
| 11. C2×#14555775 | C22 | semidirect |
| 12. C2×#14555773 | C22 | semidirect |
| 13. C2×#14555769 | C22 | semidirect |
| 17. #17984821 | C22 | semidirect |
| 18. C2×C4⋊Dic139 | C22 | semidirect |
| 21. #17984766 | C22 | semidirect |
| 22. #17984763 | C22 | semidirect |
| 24. C22⋊(C139⋊C8) | C22 | semidirect |
| 130. C22×C139 | #137 | semidirect |
| 146. C139 | #3007 | semidirect |
| 277. C22 | #17984872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| C2×#17984821 | 2 |
| #22581115 | 2 |
| #22581109 | 2 |
| #22581104 | 2 |
| #22580954 | 2 |
| #22580917 | 2 |
| C22×#41×C139 | 2 |
| #3007 | 139 |