Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22590134 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22589967 | C2 | semidirect |
| 6. #22588387 | C2 | semidirect |
| 7. C71×#1388 | C2 | semidirect |
| 170. #1388 | D71 | semidirect |
| 171. C71 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986270 | 2 |
| #22590134 | 2 |
| C2×#17985813 | 2 |
| C2×#17985811 | 2 |
| #22589967 | 2 |
| #22588387 | 2 |
| C71×#1388 | 2 |
| #13389 | 71 |