Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #22591088 | C2 | semidirect |
| 4. #22587020 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1274 | C2 | semidirect |
| 10. #17986372 | C4 | semidirect |
| 11. #17986350 | C4 | semidirect |
| 108. C42×C71 | SD16 | semidirect |
| 189. #1274 | D71 | semidirect |
| 190. C71 | #9301 | semidirect |
| 291. C42 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22591088 | 2 |
| #22589172 | 2 |
| #22587020 | 2 |
| #22586901 | 2 |
| #22586199 | 2 |
| C71×#1274 | 2 |
| #9301 | 71 |