Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589268 | C2 | semidirect |
| 3. #22589259 | C2 | semidirect |
| 4. #22587092 | C2 | semidirect |
| 5. #22587018 | C2 | semidirect |
| 6. #22586241 | C2 | semidirect |
| 7. C71×#1965 | C2 | semidirect |
| 118. M16×C71 | D8 | semidirect |
| 211. #1965 | D71 | semidirect |
| 215. C71 | #10500 | semidirect |
| 314. M16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599258 | 2 |
| #22589268 | 2 |
| #22589259 | 2 |
| #22587092 | 2 |
| #22587018 | 2 |
| #22586241 | 2 |
| C71×#1965 | 2 |
| #10500 | 71 |