Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
440 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22586359 | C2 | semidirect |
| 5. #22586358 | C2 | semidirect |
| 6. #22586357 | C2 | semidirect |
| 7. C71×#1350 | C2 | semidirect |
| 184. #1350 | D71 | semidirect |
| 185. C71 | #11712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D71 | 2 |
| #22589949 | 2 |
| #341×D71 | 2 |
| #22586359 | 2 |
| #22586358 | 2 |
| #22586357 | 2 |
| C71×#1350 | 2 |
| #11712 | 71 |