Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 3. #22589313 | C2 | semidirect |
| 4. #22587024 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1275 | C2 | semidirect |
| 11. #17986372 | C4 | semidirect |
| 12. #17986350 | C4 | semidirect |
| 107. C2×C8×C71 | SD16 | semidirect |
| 181. #1275 | D71 | semidirect |
| 182. C71 | #9289 | semidirect |
| 272. C2×C8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22597059 | 2 |
| #22589313 | 2 |
| #22587024 | 2 |
| #22586901 | 2 |
| #22586199 | 2 |
| C71×#1275 | 2 |
| #9289 | 71 |