Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#17984865 | C2 | semidirect |
| 2. C2×#17984861 | C2 | semidirect |
| 3. #22581384 | C2 | direct (N × H) |
| 4. C2×#17984788 | C2 | semidirect |
| 5. C2×#17984787 | C2 | semidirect |
| 6. C2×#17984783 | C2 | semidirect |
| 7. C2×C16×D139 | C2 | semidirect |
| 8. C2×SD32×C139 | C2 | semidirect |
| 12. #17984865 | C22 | semidirect |
| 14. #17984861 | C22 | semidirect |
| 20. #17984788 | C22 | semidirect |
| 21. #17984787 | C22 | semidirect |
| 22. #17984783 | C22 | semidirect |
| 24. C16×D139 | C22 | semidirect |
| 27. SD32×C139 | C22 | semidirect |
| 95. C2×C139 | #508 | semidirect |
| 99. C139 | C2×#508 | semidirect |
| 106. C2×SD32 | D139 | semidirect |
| 124. SD32 | C2×D139 | semidirect |
| 197. C2 | #22581384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C2×#17984861 | 2 |
| #22581384 | 2 |
| C2×#17984788 | 2 |
| C2×#17984787 | 2 |
| C2×#17984783 | 2 |
| C2×C16×D139 | 2 |
| C2×SD32×C139 | 2 |
| C2×#508 | 139 |