Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 105. M16×C71 | Q16 | semidirect |
| 185. C71 | #10199 | semidirect |
| 268. M16 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22599285 | 2 |
| #22598886 | 2 |
| #22589288 | 2 |
| #22586838 | 2 |
| #22586191 | 2 |
| C71×#1986 | 2 |
| #10199 | 71 |