Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22597352 | C2 | semidirect |
| 3. #22586938 | C2 | semidirect |
| 4. #22586775 | C2 | semidirect |
| 5. #22586250 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1469 | C2 | semidirect |
| 212. #1469 | D71 | semidirect |
| 215. C71 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597830 | 2 |
| #22597352 | 2 |
| #22586938 | 2 |
| #22586775 | 2 |
| #22586250 | 2 |
| #22586231 | 2 |
| C71×#1469 | 2 |
| #9349 | 71 |