Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #22599278 | C2 | semidirect |
| 3. #22589285 | C2 | semidirect |
| 4. #22589266 | C2 | semidirect |
| 5. #22586835 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#3246 | C2 | semidirect |
| 95. #11765849 | SD16 | semidirect |
| 210. #3246 | D71 | semidirect |
| 217. C71 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22598793 | 2 |
| #22589285 | 2 |
| #22589266 | 2 |
| #22586835 | 2 |
| #22586190 | 2 |
| C71×#3246 | 2 |
| #10194 | 71 |