Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 3. #22587865 | C2 | semidirect |
| 5. #22586321 | C2 | semidirect |
| 6. #22586310 | C2 | semidirect |
| 7. C71×#2225 | C2 | semidirect |
| 143. #2225 | D71 | semidirect |
| 148. C71 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601417 | 2 |
| #22590579 | 2 |
| #22587865 | 2 |
| #22586384 | 2 |
| #22586321 | 2 |
| #22586310 | 2 |
| C71×#2225 | 2 |
| #12389 | 71 |