Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 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 |
|---|---|---|
| 1. #22599647 | C2 | semidirect |
| 2. #22599258 | C2 | semidirect |
| 3. #22589268 | C2 | semidirect |
| 4. #22589259 | C2 | semidirect |
| 5. #22586835 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#3151 | C2 | semidirect |
| 126. M16×C71 | D8 | semidirect |
| 223. #3151 | 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 |
| #22599258 | 2 |
| #22589268 | 2 |
| #22589259 | 2 |
| #22586835 | 2 |
| #22586191 | 2 |
| C71×#3151 | 2 |
| #10192 | 71 |