Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 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. #22597434 | C2 | semidirect |
| 3. #22587071 | C2 | semidirect |
| 6. #22586250 | C2 | semidirect |
| 7. C71×#1287 | C2 | semidirect |
| 175. #1287 | D71 | semidirect |
| 176. C71 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598440 | 2 |
| #22597434 | 2 |
| #22587071 | 2 |
| #22586766 | 2 |
| #22586680 | 2 |
| #22586250 | 2 |
| C71×#1287 | 2 |
| #9530 | 71 |