Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17985823 | C2 | semidirect |
| 5. #22586440 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#1953 | C2 | semidirect |
| 20. #17985805 | C4 | semidirect |
| 45. C2×C71⋊C16 | C2×C4 | semidirect |
| 59. #108×C71 | C2×C4 | semidirect |
| 156. #1953 | D71 | semidirect |
| 159. C71 | #12949 | semidirect |
| 207. #108 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597225 | 2 |
| C2×#17985823 | 2 |
| #22590087 | 2 |
| #22590067 | 2 |
| #22586440 | 2 |
| #22586426 | 2 |
| C71×#1953 | 2 |
| #12949 | 71 |