Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
220 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22587238 | C2 | semidirect |
| 3. #22586411 | C2 | semidirect |
| 4. #22586303 | C2 | semidirect |
| 6. #22586257 | C2 | semidirect |
| 53. C71⋊C16 | M16 | semidirect |
| 113. C71 | #12084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556072 | 2 |
| #22587238 | 2 |
| #22586411 | 2 |
| #22586303 | 2 |
| #22586301 | 2 |
| #22586257 | 2 |
| C71×#1589 | 2 |
| #12084 | 71 |