Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#17986442 | C2 | semidirect |
| 3. #22597995 | C2 | semidirect |
| 4. #22590293 | C2 | semidirect |
| 5. #22590077 | C2 | semidirect |
| 6. C71×#2115 | C2 | semidirect |
| 15. C22×Dic284 | C22 | semidirect |
| 18. #17986442 | C22 | semidirect |
| 21. #17986257 | C22 | semidirect |
| 23. #17986037 | C22 | semidirect |
| 25. #17985810 | C22 | semidirect |
| 27. C2×M32×C71 | C22 | semidirect |
| 28. #349×C71 | C22 | semidirect |
| 203. #2115 | D71 | semidirect |
| 204. C71 | #33532 | semidirect |
| 220. C2×M32 | C2×D71 | semidirect |
| 226. #349 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603114 | 2 |
| C2×#17986442 | 2 |
| #22597995 | 2 |
| #22590293 | 2 |
| #22590077 | 2 |
| C71×#2115 | 2 |
| #33532 | 71 |