Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 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. #364×D71 | C2 | semidirect |
| 3. #22586381 | C2 | semidirect |
| 4. #22586380 | C2 | semidirect |
| 5. C71×#1359 | C2 | semidirect |
| 139. #1359 | D71 | semidirect |
| 140. C71 | #11922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598763 | 2 |
| #364×D71 | 2 |
| #22586381 | 2 |
| #22586380 | 2 |
| C71×#1359 | 2 |
| #11922 | 71 |