Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590098 | C2 | semidirect |
| 5. #22588463 | C2 | semidirect |
| 6. #22586451 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 11. #17986120 | C4 | semidirect |
| 147. #1382 | D71 | semidirect |
| 148. C71 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597256 | 2 |
| #22590098 | 2 |
| #22590075 | 2 |
| C2×#17985807 | 2 |
| #22588463 | 2 |
| #22586451 | 2 |
| C71×#1382 | 2 |
| #12830 | 71 |