Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #22596975 | C2 | semidirect |
| 3. #22589188 | C2 | semidirect |
| 4. #22589178 | C2 | semidirect |
| 5. #22588268 | C2 | semidirect |
| 6. #22588260 | C2 | semidirect |
| 7. C71×#1785 | C2 | semidirect |
| 16. #17986022 | C22 | semidirect |
| 17. C2×#14556047 | C22 | semidirect |
| 18. C2×#14556045 | C22 | semidirect |
| 22. M16×Dic71 | C22 | semidirect |
| 24. C2×#101×C71 | C22 | semidirect |
| 25. C2×#100×C71 | C22 | semidirect |
| 187. #1785 | D71 | semidirect |
| 189. C71 | #21801 | semidirect |
| 201. C2×#101 | C2×D71 | semidirect |
| 205. C2×#100 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986563 | 2 |
| #22596975 | 2 |
| #22589188 | 2 |
| #22589178 | 2 |
| #22588268 | 2 |
| #22588260 | 2 |
| C71×#1785 | 2 |
| #21801 | 71 |