Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 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. #22589904 | C2 | semidirect |
| 3. #22589878 | C2 | semidirect |
| 5. #22586164 | C2 | semidirect |
| 7. C71×#1272 | C2 | semidirect |
| 191. #1272 | D71 | semidirect |
| 194. C71 | #7834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596322 | 2 |
| #22589904 | 2 |
| #22589878 | 2 |
| #22589872 | 2 |
| #22586164 | 2 |
| #22586160 | 2 |
| C71×#1272 | 2 |
| #7834 | 71 |