Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17986415 | C2 | semidirect |
| 2. #22597984 | C2 | semidirect |
| 3. #22590440 | C2 | semidirect |
| 4. #22590423 | C2 | semidirect |
| 5. #22590124 | C2 | semidirect |
| 6. #22590056 | C2 | semidirect |
| 7. C22×D16×C71 | C2 | semidirect |
| 12. C2×#14556067 | C22 | semidirect |
| 13. C2×C16×D71 | C22 | semidirect |
| 15. #17986232 | C22 | semidirect |
| 18. #17985827 | C22 | semidirect |
| 19. #17985825 | C22 | semidirect |
| 20. #17985800 | C22 | semidirect |
| 52. C2×C16×C71 | D4 | semidirect |
| 130. C22×D16 | D71 | semidirect |
| 137. C71 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986415 | 2 |
| #22597984 | 2 |
| #22590440 | 2 |
| #22590423 | 2 |
| #22590124 | 2 |
| #22590056 | 2 |
| C22×D16×C71 | 2 |
| #33607 | 71 |