Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1264 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1264 conjugacy classes of subgroups — too many to draw. Only its 203 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×#17986318 | C2 | semidirect |
| 3. C2×#17985938 | C2 | semidirect |
| 4. #22587379 | C2 | direct (N × H) |
| 5. C2×#17985734 | C2 | semidirect |
| 6. C2×#324×C71 | C2 | semidirect |
| 17. #17986318 | C22 | semidirect |
| 21. #17985938 | C22 | semidirect |
| 25. #17985734 | C22 | semidirect |
| 28. #324×C71 | C22 | semidirect |
| 204. C2×C71 | #1616 | semidirect |
| 214. C2×#324 | D71 | semidirect |
| 215. C71 | C2×#1616 | semidirect |
| 237. #324 | C2×D71 | semidirect |
| 413. C2 | #22587379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986580 | 2 |
| C2×#17986318 | 2 |
| C2×#17985938 | 2 |
| #22587379 | 2 |
| C2×#17985734 | 2 |
| C2×#324×C71 | 2 |
| C2×#1616 | 71 |