Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22590274 | C2 | semidirect |
| 4. #22586359 | C2 | semidirect |
| 5. #22586358 | C2 | semidirect |
| 7. C71×#2188 | C2 | semidirect |
| 174. #2188 | D71 | semidirect |
| 179. C71 | #12112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599230 | 2 |
| #22590274 | 2 |
| #22589459 | 2 |
| #22586359 | 2 |
| #22586358 | 2 |
| #22586265 | 2 |
| C71×#2188 | 2 |
| #12112 | 71 |