Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984863 | C2 | semidirect |
| 3. #22581504 | C2 | semidirect |
| 4. #22581502 | C2 | semidirect |
| 5. #22581346 | C2 | semidirect |
| 6. #22581345 | C2 | semidirect |
| 7. #22581343 | C2 | semidirect |
| 8. #22581342 | C2 | semidirect |
| 9. #22581339 | C2 | semidirect |
| 10. #97×D139 | C2 | semidirect |
| 11. #497×C139 | C2 | semidirect |
| 65. C8×D139 | D4 | semidirect |
| 133. C139 | #3150 | semidirect |
| 141. #497 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C2×#17984863 | 2 |
| #22581504 | 2 |
| #22581502 | 2 |
| #22581346 | 2 |
| #22581345 | 2 |
| #22581343 | 2 |
| #22581342 | 2 |
| #22581339 | 2 |
| #97×D139 | 2 |
| #497×C139 | 2 |
| #3150 | 139 |