Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581677 | C2 | semidirect |
| 3. #22581290 | C2 | semidirect |
| 4. #22581280 | C2 | semidirect |
| 5. #22581235 | C2 | semidirect |
| 6. #22581230 | C2 | semidirect |
| 7. #22581200 | C2 | semidirect |
| 8. C4×#14555774 | C2 | semidirect |
| 9. #22581032 | C2 | semidirect |
| 10. #22580994 | C2 | semidirect |
| 11. #500×C139 | C2 | semidirect |
| 99. C8×C139 | #41 | semidirect |
| 122. C139 | #3353 | semidirect |
| 126. #500 | D139 | semidirect |
| 222. C8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581677 | 2 |
| #22581606 | 2 |
| #22581290 | 2 |
| #22581280 | 2 |
| #22581235 | 2 |
| #22581230 | 2 |
| #22581200 | 2 |
| C4×#14555774 | 2 |
| #22581032 | 2 |
| #22580994 | 2 |
| #500×C139 | 2 |
| #3353 | 139 |