Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
130 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22586416 | C2 | semidirect |
| 3. C71×#1422 | C2 | semidirect |
| 64. #1422 | D71 | semidirect |
| 66. C71 | #7447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590601 | 2 |
| #22586416 | 2 |
| C71×#1422 | 2 |
| #7447 | 71 |