Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22589813 | C2 | semidirect |
| 4. #22589750 | C2 | semidirect |
| 5. #22586165 | C2 | semidirect |
| 6. #22586164 | C2 | semidirect |
| 202. C71 | #7789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22595357 | 2 |
| #22589868 | 2 |
| #22589813 | 2 |
| #22589750 | 2 |
| #22586165 | 2 |
| #22586164 | 2 |
| C71×#1270 | 2 |
| #7789 | 71 |