Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22586200 | C2 | semidirect |
| 4. #22586185 | C2 | semidirect |
| 5. C71×#1849 | C2 | semidirect |
| 113. #1849 | D71 | semidirect |
| 117. C71 | #10631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589164 | 2 |
| #22587009 | 2 |
| #22586200 | 2 |
| #22586185 | 2 |
| C71×#1849 | 2 |
| #10631 | 71 |