Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
908 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #22588276 | C2 | semidirect |
| 4. #22586220 | C2 | semidirect |
| 11. #17985911 | C4 | semidirect |
| 24. C22×Dic142 | C2×C4 | semidirect |
| 41. C71⋊#95 | C2×C4 | semidirect |
| 120. C23×C71 | #103 | semidirect |
| 204. C71 | #9013 | semidirect |
| 319. C23 | #14556053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985911 | 2 |
| #22590954 | 2 |
| #22588276 | 2 |
| #22586220 | 2 |
| C2×#323×C71 | 2 |
| #9013 | 71 |