Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
500 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 87. C2×Dic142 | Q16 | semidirect |
| 208. C71 | #10003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598141 | 2 |
| #22593706 | 2 |
| #22586904 | 2 |
| #22586769 | 2 |
| #22586736 | 2 |
| #22586199 | 2 |
| C71×#3104 | 2 |
| #10003 | 71 |