Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22587103 | C2 | semidirect |
| 4. #22586209 | C2 | semidirect |
| 5. C71×#1568 | C2 | semidirect |
| 136. #1568 | D71 | semidirect |
| 139. C71 | #8624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986078 | 2 |
| #22587103 | 2 |
| #22586680 | 2 |
| #22586209 | 2 |
| C71×#1568 | 2 |
| #8624 | 71 |