Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22588511 | C2 | semidirect |
| 3. #22586795 | C2 | semidirect |
| 6. C2×#17985720 | C2 | semidirect |
| 7. C71×#1493 | C2 | semidirect |
| 162. #1493 | D71 | semidirect |
| 166. C71 | #9858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598665 | 2 |
| #22588511 | 2 |
| #22586795 | 2 |
| #22586792 | 2 |
| #22586790 | 2 |
| C2×#17985720 | 2 |
| C71×#1493 | 2 |
| #9858 | 71 |