Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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×#17986439 | C2 | semidirect |
| 2. C22×#14556073 | C2 | semidirect |
| 4. #22597207 | C2 | semidirect |
| 5. #22590405 | C2 | semidirect |
| 6. #22590379 | C2 | semidirect |
| 7. #22590098 | C2 | semidirect |
| 8. #22590055 | C2 | semidirect |
| 9. C71×#2138 | C2 | semidirect |
| 16. C2×#14556074 | C22 | semidirect |
| 19. C2×#14556072 | C22 | semidirect |
| 25. #17986093 | C22 | semidirect |
| 28. Dic71⋊C16 | C22 | semidirect |
| 33. #358×C71 | C22 | semidirect |
| 34. #357×C71 | C22 | semidirect |
| 40. C2×Dic284 | D4 | semidirect |
| 185. #2138 | D71 | semidirect |
| 186. C71 | #33587 | semidirect |
| 209. #358 | C2×D71 | semidirect |
| 211. #357 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986439 | 2 |
| C22×#14556073 | 2 |
| #22598827 | 2 |
| #22597207 | 2 |
| #22590405 | 2 |
| #22590379 | 2 |
| #22590098 | 2 |
| #22590055 | 2 |
| C71×#2138 | 2 |
| #33587 | 71 |