Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 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. #22596948 | C2 | semidirect |
| 3. C2×#17985806 | C2 | semidirect |
| 4. C2×#17985784 | C2 | semidirect |
| 5. #22586452 | C2 | semidirect |
| 6. #22586433 | C2 | semidirect |
| 7. C71×#2143 | C2 | semidirect |
| 181. #2143 | D71 | semidirect |
| 186. C71 | #12995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598056 | 2 |
| #22596948 | 2 |
| C2×#17985806 | 2 |
| C2×#17985784 | 2 |
| #22586452 | 2 |
| #22586433 | 2 |
| C71×#2143 | 2 |
| #12995 | 71 |