Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 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. #22590105 | C2 | semidirect |
| 5. #22588463 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#1384 | C2 | semidirect |
| 11. #17986110 | C4 | semidirect |
| 144. #1384 | D71 | semidirect |
| 145. C71 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597191 | 2 |
| #22590105 | 2 |
| C2×#17985813 | 2 |
| #22590055 | 2 |
| #22588463 | 2 |
| #22586456 | 2 |
| C71×#1384 | 2 |
| #12826 | 71 |