Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #22589066 | C2 | semidirect |
| 5. #22586440 | C2 | semidirect |
| 6. #22586421 | C2 | semidirect |
| 7. C2×#365×C71 | C2 | semidirect |
| 17. #17985810 | C4 | semidirect |
| 70. Dic284 | C4⋊C4 | semidirect |
| 74. D568 | C4⋊C4 | semidirect |
| 158. C2×#365 | D71 | semidirect |
| 164. C71 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986115 | 2 |
| C2×#17985810 | 2 |
| C2×#17985808 | 2 |
| #22589066 | 2 |
| #22586440 | 2 |
| #22586421 | 2 |
| C2×#365×C71 | 2 |
| #12950 | 71 |