Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
448 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22597415 | C2 | semidirect |
| 3. #22586952 | C2 | semidirect |
| 4. #22586951 | C2 | semidirect |
| 5. #22586203 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 7. C71×#1496 | C2 | semidirect |
| 180. #1496 | D71 | semidirect |
| 183. C71 | #9283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599269 | 2 |
| #22597415 | 2 |
| #22586952 | 2 |
| #22586951 | 2 |
| #22586203 | 2 |
| #22586170 | 2 |
| C71×#1496 | 2 |
| #9283 | 71 |