Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #22598056 | C2 | semidirect |
| 2. C2×#17985806 | C2 | semidirect |
| 3. #22589955 | C2 | semidirect |
| 4. #22586444 | C2 | semidirect |
| 5. C71×#3414 | C2 | semidirect |
| 137. #3414 | D71 | semidirect |
| 142. C71 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598056 | 2 |
| C2×#17985806 | 2 |
| #22589955 | 2 |
| #22586444 | 2 |
| C71×#3414 | 2 |
| #13312 | 71 |