Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 408 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. C2×#17985814 | C2 | semidirect |
| 4. C2×#17985776 | C2 | semidirect |
| 6. #22589209 | C2 | semidirect |
| 7. C2×#365×C71 | C2 | semidirect |
| 12. C2×Dic568 | C4 | semidirect |
| 13. C2×#14556073 | C4 | semidirect |
| 166. C2×#365 | D71 | semidirect |
| 172. C71 | #13250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986442 | 2 |
| C2×#17985814 | 2 |
| C2×#17985808 | 2 |
| C2×#17985776 | 2 |
| #22589231 | 2 |
| #22589209 | 2 |
| C2×#365×C71 | 2 |
| #13250 | 71 |