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×#17984867 | C2 | semidirect |
| 3. C22×#14555774 | C2 | semidirect |
| 4. #22581522 | C2 | semidirect |
| 5. #22581099 | C2 | semidirect |
| 6. #22581093 | C2 | semidirect |
| 7. #22580961 | C2 | semidirect |
| 8. #22580919 | C2 | semidirect |
| 9. #416×C139 | C2 | semidirect |
| 15. C2×#14555784 | C22 | semidirect |
| 18. C2×Q8×D139 | C22 | semidirect |
| 30. #17984765 | C22 | semidirect |
| 31. (C2×D139)⋊C8 | C22 | semidirect |
| 35. #103×C139 | C22 | semidirect |
| 36. #102×C139 | C22 | semidirect |
| 49. C2×Dic278 | D4 | semidirect |
| 72. #41×C139 | D4 | semidirect |
| 145. C139 | #3010 | semidirect |
| 154. #416 | D139 | semidirect |
| 180. #103 | C2×D139 | semidirect |
| 181. #102 | C2×D139 | semidirect |
| 191. #41 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C2×#17984867 | 2 |
| C22×#14555774 | 2 |
| #22581522 | 2 |
| #22581099 | 2 |
| #22581093 | 2 |
| #22580961 | 2 |
| #22580919 | 2 |
| #416×C139 | 2 |
| #3010 | 139 |