Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
490 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 81. #11765849 | Q16 | semidirect |
| 187. C71 | #10203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22598882 | 2 |
| #22589285 | 2 |
| #22589264 | 2 |
| #22586840 | 2 |
| #22586189 | 2 |
| C71×#3230 | 2 |
| #10203 | 71 |