Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581581 | C2 | semidirect |
| 3. #22581318 | C2 | semidirect |
| 4. #22581313 | C2 | semidirect |
| 5. #22581308 | C2 | semidirect |
| 6. #22581300 | C2 | semidirect |
| 7. #22580959 | C2 | semidirect |
| 8. #22580955 | C2 | semidirect |
| 9. #22580950 | C2 | semidirect |
| 10. C2×#17984764 | C2 | semidirect |
| 11. #405×C139 | C2 | semidirect |
| 14. #17984842 | C22 | semidirect |
| 17. #17984834 | C22 | semidirect |
| 26. #17984767 | C22 | semidirect |
| 27. #17984767 | C22 | semidirect |
| 28. #17984767 | C22 | semidirect |
| 33. #17984764 | C22 | semidirect |
| 34. #17984764 | C22 | semidirect |
| 35. #17984764 | C22 | semidirect |
| 39. #97×C139 | C22 | semidirect |
| 40. C4×C8×C139 | C22 | semidirect |
| 135. C139 | #3136 | semidirect |
| 147. #405 | D139 | semidirect |
| 175. #97 | C2×D139 | semidirect |
| 176. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581522 | 2 |
| #22581318 | 2 |
| #22581313 | 2 |
| #22581308 | 2 |
| #22581300 | 2 |
| #22580959 | 2 |
| #22580955 | 2 |
| #22580950 | 2 |
| C2×#17984764 | 2 |
| #405×C139 | 2 |
| #3136 | 139 |