Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984875 | C2 | semidirect |
| 3. C22×#14555774 | C2 | semidirect |
| 4. C2×#17984848 | C2 | semidirect |
| 5. #22581217 | C2 | direct (N × H) |
| 6. C2×#17984760 | C2 | semidirect |
| 7. C2×#17984758 | C2 | semidirect |
| 8. C2×#108×C139 | C2 | semidirect |
| 13. #17984875 | C22 | semidirect |
| 22. C2×#14555774 | C22 | semidirect |
| 25. #17984848 | C22 | semidirect |
| 29. #17984760 | C22 | semidirect |
| 30. #17984758 | C22 | semidirect |
| 34. #108×C139 | C22 | semidirect |
| 134. C2×C139 | #471 | semidirect |
| 138. C139 | C2×#471 | semidirect |
| 145. C2×#108 | D139 | semidirect |
| 171. #108 | C2×D139 | semidirect |
| 275. C2 | #22581217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| C2×#17984870 | 2 |
| C22×#14555774 | 2 |
| C2×#17984848 | 2 |
| #22581217 | 2 |
| C2×#17984760 | 2 |
| C2×#17984758 | 2 |
| C2×#108×C139 | 2 |
| C2×#471 | 139 |