Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
426 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22588455 | C2 | semidirect |
| 3. #22588087 | C2 | semidirect |
| 4. #22586164 | C2 | semidirect |
| 5. #22586162 | C2 | semidirect |
| 201. C71 | #7706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596704 | 2 |
| #22588455 | 2 |
| #22588087 | 2 |
| #22586164 | 2 |
| #22586162 | 2 |
| #22586161 | 2 |
| C71×#1270 | 2 |
| #7706 | 71 |