Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
302 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22590525 | C2 | semidirect |
| 3. #22589846 | C2 | semidirect |
| 4. #22586356 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586281 | C2 | semidirect |
| 7. C71×#2232 | C2 | semidirect |
| 151. #2232 | D71 | semidirect |
| 156. C71 | #12294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599774 | 2 |
| #22590525 | 2 |
| #22589846 | 2 |
| #22586356 | 2 |
| #22586355 | 2 |
| #22586281 | 2 |
| C71×#2232 | 2 |
| #12294 | 71 |