Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 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. C2×#17984841 | C2 | semidirect |
| 3. #22581242 | C2 | direct (N × H) |
| 4. C2×#17984773 | C2 | semidirect |
| 5. C2×Dic139⋊C8 | C2 | semidirect |
| 8. C2×#106×C139 | C2 | semidirect |
| 14. #17984841 | C22 | semidirect |
| 21. #17984773 | C22 | semidirect |
| 22. Dic139⋊C8 | C22 | semidirect |
| 28. #106×C139 | C22 | semidirect |
| 34. C2×D556 | Q8 | semidirect |
| 65. D556 | C2×Q8 | semidirect |
| 100. C2×C139 | #476 | semidirect |
| 105. C139 | C2×#476 | semidirect |
| 111. C2×#106 | D139 | semidirect |
| 131. #106 | C2×D139 | semidirect |
| 207. C2 | #22581242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984841 | 2 |
| C2×#17984804 | 2 |
| #22581242 | 2 |
| C2×#17984773 | 2 |
| C2×Dic139⋊C8 | 2 |
| C2×#17984764 | 2 |
| C2×#17984762 | 2 |
| C2×#106×C139 | 2 |
| C2×#476 | 139 |