Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #22581565 | C2 | direct (N × H) |
| 2. C2×#17984842 | C2 | semidirect |
| 4. C2×#17984834 | C2 | semidirect |
| 5. C2×#17984832 | C2 | semidirect |
| 7. C2×C4×Dic278 | C2 | semidirect |
| 10. #17984842 | C22 | semidirect |
| 12. #17984834 | C22 | semidirect |
| 13. #17984832 | C22 | semidirect |
| 15. C4×Dic278 | C22 | semidirect |
| 82. C2×C139 | #541 | semidirect |
| 85. C139 | C2×#541 | semidirect |
| 168. C2 | #22581565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581565 | 2 |
| C2×#17984842 | 2 |
| C2×#17984835 | 2 |
| C2×#17984834 | 2 |
| C2×#17984832 | 2 |
| C2×#17984821 | 2 |
| C2×C4×Dic278 | 2 |
| C2×#117×C139 | 2 |
| C2×#541 | 139 |