Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
524 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22589289 | C2 | semidirect |
| 5. #22586839 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#3165 | C2 | semidirect |
| 107. M16×C71 | SD16 | semidirect |
| 191. #3165 | D71 | semidirect |
| 196. C71 | #10197 | semidirect |
| 286. M16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599652 | 2 |
| #22599265 | 2 |
| #22589289 | 2 |
| #22589259 | 2 |
| #22586839 | 2 |
| #22586191 | 2 |
| C71×#3165 | 2 |
| #10197 | 71 |