Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
550 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 550 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 |
|---|---|---|
| 3. #22587012 | C2 | semidirect |
| 5. #22586664 | C2 | semidirect |
| 6. #22586237 | C2 | semidirect |
| 7. C2×#462×C71 | C2 | semidirect |
| 210. C2×#462 | D71 | semidirect |
| 215. C71 | #10185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599461 | 2 |
| #22597812 | 2 |
| #22587012 | 2 |
| #22586738 | 2 |
| #22586664 | 2 |
| #22586237 | 2 |
| C2×#462×C71 | 2 |
| #10185 | 71 |