Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
480 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597209 | C2 | semidirect |
| 3. C2×#17985816 | C2 | semidirect |
| 6. #22586436 | C2 | semidirect |
| 7. C71×#1379 | C2 | semidirect |
| 13. C2×#14556073 | C4 | semidirect |
| 166. #1379 | D71 | semidirect |
| 167. C71 | #13018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556073 | 2 |
| #22597209 | 2 |
| C2×#17985816 | 2 |
| #22590057 | 2 |
| #22589250 | 2 |
| #22586436 | 2 |
| C71×#1379 | 2 |
| #13018 | 71 |