Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
640 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590031 | C2 | semidirect |
| 3. #22589991 | C2 | semidirect |
| 4. #22588315 | C2 | semidirect |
| 5. #22586470 | C2 | semidirect |
| 6. #22586462 | C2 | semidirect |
| 7. C71×#2889 | C2 | semidirect |
| 8. C2×#14556153 | C4 | semidirect |
| 9. C22×#11765852 | C4 | semidirect |
| 17. #17986008 | C4 | semidirect |
| 18. #17985995 | C4 | semidirect |
| 247. #2889 | D71 | semidirect |
| 253. C71 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597626 | 2 |
| #22590031 | 2 |
| #22589991 | 2 |
| #22588315 | 2 |
| #22586470 | 2 |
| #22586462 | 2 |
| C71×#2889 | 2 |
| #13098 | 71 |