Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22590508 | C2 | semidirect |
| 3. #22587974 | C2 | semidirect |
| 4. #22586378 | C2 | semidirect |
| 5. #22586316 | C2 | semidirect |
| 6. #22586315 | C2 | semidirect |
| 7. C71×#2230 | C2 | semidirect |
| 164. #2230 | D71 | semidirect |
| 169. C71 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600145 | 2 |
| #22590508 | 2 |
| #22587974 | 2 |
| #22586378 | 2 |
| #22586316 | 2 |
| #22586315 | 2 |
| C71×#2230 | 2 |
| #12367 | 71 |