Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 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. C2×#17984867 | C2 | semidirect |
| 2. C2×#17984831 | C2 | semidirect |
| 3. #22581126 | C2 | direct (N × H) |
| 4. C2×#17984769 | C2 | semidirect |
| 5. C2×#17984761 | C2 | semidirect |
| 6. C2×2−1+4×C139 | C2 | semidirect |
| 9. #17984867 | C22 | semidirect |
| 14. #17984831 | C22 | semidirect |
| 17. #17984769 | C22 | semidirect |
| 18. #17984761 | C22 | semidirect |
| 21. 2−1+4×C139 | C22 | semidirect |
| 114. C2×C139 | #454 | semidirect |
| 117. C139 | C2×#454 | semidirect |
| 119. C2×2−1+4 | D139 | semidirect |
| 127. 2−1+4 | C2×D139 | semidirect |
| 233. C2 | #22581126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| C2×#17984831 | 2 |
| #22581126 | 2 |
| C2×#17984769 | 2 |
| C2×#17984761 | 2 |
| C2×2−1+4×C139 | 2 |
| C2×#454 | 139 |