Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22590135 | C2 | semidirect |
| 3. C2×#17985828 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 19. #17985784 | C4 | semidirect |
| 143. #1389 | D71 | semidirect |
| 145. C71 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596948 | 2 |
| #22590135 | 2 |
| C2×#17985828 | 2 |
| C2×#17985784 | 2 |
| #22588391 | 2 |
| #22586435 | 2 |
| C71×#1389 | 2 |
| #12927 | 71 |