Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#17985828 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22589939 | C2 | semidirect |
| 5. #22589251 | C2 | semidirect |
| 6. #22589248 | C2 | semidirect |
| 7. C2×#361×C71 | C2 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 168. C2×#361 | D71 | semidirect |
| 172. C71 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| C2×#17985828 | 2 |
| C2×#17985813 | 2 |
| #22589939 | 2 |
| #22589251 | 2 |
| #22589248 | 2 |
| C2×#361×C71 | 2 |
| #13245 | 71 |