Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
830 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #22586222 | C2 | semidirect |
| 4. #22586221 | C2 | semidirect |
| 5. C71×#1295 | C2 | semidirect |
| 12. #97×D71 | C4 | semidirect |
| 34. #14556039 | C2×C4 | semidirect |
| 42. #97×C71 | C2×C4 | semidirect |
| 124. D71 | #1295 | direct (N × H) |
| 129. #1295 | D71 | direct (N × H) |
| 130. C71 | C2×#1295 | semidirect |
| 165. #97 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D71 | 2 |
| #382×D71 | 2 |
| #22586222 | 2 |
| #22586221 | 2 |
| C71×#1295 | 2 |
| C2×#1295 | 71 |