Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 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. #22589329 | C2 | semidirect |
| 3. #22589262 | C2 | semidirect |
| 6. #22586242 | C2 | semidirect |
| 7. C71×#1565 | C2 | semidirect |
| 108. M16×C71 | SD16 | semidirect |
| 191. #1565 | D71 | semidirect |
| 194. C71 | #10501 | semidirect |
| 282. M16 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22589329 | 2 |
| #22589262 | 2 |
| #22589259 | 2 |
| #22587015 | 2 |
| #22586242 | 2 |
| C71×#1565 | 2 |
| #10501 | 71 |