Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 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 |
|---|---|---|
| 2. #22599481 | C2 | semidirect |
| 4. #22589292 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1986 | C2 | semidirect |
| 111. M16×C71 | SD16 | semidirect |
| 197. #1986 | D71 | semidirect |
| 200. C71 | #10206 | semidirect |
| 293. M16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599652 | 2 |
| #22599481 | 2 |
| #22598799 | 2 |
| #22589292 | 2 |
| #22586834 | 2 |
| #22586191 | 2 |
| C71×#1986 | 2 |
| #10206 | 71 |