Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588376 | C2 | semidirect |
| 3. #22588119 | C2 | semidirect |
| 4. #22586860 | C2 | semidirect |
| 7. C71×#1472 | C2 | semidirect |
| 8. C22×#11765852 | C4 | semidirect |
| 16. C2×#14556059 | C4 | semidirect |
| 17. C2×#14556052 | C4 | semidirect |
| 18. C2×#14556048 | C4 | semidirect |
| 221. #1472 | D71 | semidirect |
| 223. C71 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986230 | 2 |
| #22588376 | 2 |
| #22588119 | 2 |
| #22586860 | 2 |
| #22586857 | 2 |
| #22586699 | 2 |
| C71×#1472 | 2 |
| #9816 | 71 |