Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22589325 | C2 | semidirect |
| 3. #22588367 | C2 | semidirect |
| 4. #22588118 | C2 | semidirect |
| 5. #22586911 | C2 | semidirect |
| 8. C22×#11765853 | C4 | semidirect |
| 16. C2×#14556059 | C4 | semidirect |
| 17. C2×#14556051 | C4 | semidirect |
| 18. C2×#14556049 | C4 | semidirect |
| 194. C71⋊C8 | #99 | semidirect |
| 239. C71 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986226 | 2 |
| #22589325 | 2 |
| #22588367 | 2 |
| #22588118 | 2 |
| #22586911 | 2 |
| #22586908 | 2 |
| C71×#1964 | 2 |
| #9786 | 71 |