Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22590139 | C2 | semidirect |
| 3. #22586393 | C2 | semidirect |
| 4. #22586382 | C2 | semidirect |
| 5. C71×#1564 | C2 | semidirect |
| 139. #1564 | D71 | semidirect |
| 142. C71 | #11943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598910 | 2 |
| #22590139 | 2 |
| #22586393 | 2 |
| #22586382 | 2 |
| C71×#1564 | 2 |
| #11943 | 71 |