Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17985821 | C2 | semidirect |
| 3. C2×#17985815 | C2 | semidirect |
| 5. C2×#17985777 | C2 | semidirect |
| 7. C71×#1971 | C2 | semidirect |
| 11. C2×#14556074 | C4 | semidirect |
| 12. C2×#14556071 | C4 | semidirect |
| 171. #1971 | 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×#17986440 | 2 |
| C2×#17985821 | 2 |
| C2×#17985815 | 2 |
| C2×#17985808 | 2 |
| C2×#17985777 | 2 |
| #22589233 | 2 |
| C71×#1971 | 2 |
| #13250 | 71 |