Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
490 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22588801 | C2 | semidirect |
| 3. #22588779 | C2 | semidirect |
| 4. #22588547 | C2 | semidirect |
| 5. #22586909 | C2 | semidirect |
| 6. #22586247 | C2 | semidirect |
| 7. C71×#1471 | C2 | semidirect |
| 230. #1471 | D71 | semidirect |
| 232. C71 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599137 | 2 |
| #22588801 | 2 |
| #22588779 | 2 |
| #22588547 | 2 |
| #22586909 | 2 |
| #22586247 | 2 |
| C71×#1471 | 2 |
| #10560 | 71 |