Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984889 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. C22×#14555774 | C2 | semidirect |
| 4. #22581517 | C2 | semidirect |
| 5. #22581100 | C2 | semidirect |
| 6. #22581094 | C2 | semidirect |
| 7. #22580963 | C2 | semidirect |
| 8. #22580950 | C2 | semidirect |
| 9. #408×C139 | C2 | semidirect |
| 13. C2×#14555785 | C22 | semidirect |
| 17. C22×Dic278 | C22 | semidirect |
| 30. #17984767 | C22 | semidirect |
| 31. #17984767 | C22 | semidirect |
| 32. #17984764 | C22 | semidirect |
| 36. C22⋊C8×C139 | C22 | semidirect |
| 41. #14555785 | D4 | semidirect |
| 49. C2×Dic278 | D4 | semidirect |
| 145. C139 | #3010 | semidirect |
| 155. #408 | D139 | semidirect |
| 182. C22⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C2×#17984870 | 2 |
| C22×#14555774 | 2 |
| #22581517 | 2 |
| #22581100 | 2 |
| #22581094 | 2 |
| #22580963 | 2 |
| #22580950 | 2 |
| #408×C139 | 2 |
| #3010 | 139 |