Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
524 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 3. #22598886 | C2 | semidirect |
| 4. #22589288 | C2 | semidirect |
| 5. #22586838 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 112. M16×C71 | SD16 | semidirect |
| 196. C71 | #10197 | semidirect |
| 286. M16 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599656 | 2 |
| #22599262 | 2 |
| #22598886 | 2 |
| #22589288 | 2 |
| #22586838 | 2 |
| #22586191 | 2 |
| C71×#1980 | 2 |
| #10197 | 71 |