Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
486 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22588376 | C2 | semidirect |
| 4. #22586216 | C2 | semidirect |
| 104. C23×C71 | #108 | semidirect |
| 123. C2×C4×C71 | #108 | semidirect |
| 169. C71 | #8612 | semidirect |
| 268. C23 | #14556063 | semidirect |
| 287. C2×C4 | #14556063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C71⋊C8 | 2 |
| #22588376 | 2 |
| #22586678 | 2 |
| #22586216 | 2 |
| C71×#1465 | 2 |
| #8612 | 71 |