Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 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 |
|---|---|---|
| 1. #22599647 | C2 | semidirect |
| 2. #22599255 | C2 | semidirect |
| 3. #22598792 | C2 | semidirect |
| 4. #22589267 | C2 | semidirect |
| 5. #22586834 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1980 | C2 | semidirect |
| 123. M16×C71 | D8 | semidirect |
| 225. #1980 | D71 | semidirect |
| 228. C71 | #10192 | semidirect |
| 337. M16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599647 | 2 |
| #22599255 | 2 |
| #22598792 | 2 |
| #22589267 | 2 |
| #22586834 | 2 |
| #22586191 | 2 |
| C71×#1980 | 2 |
| #10192 | 71 |