Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17985828 | C2 | semidirect |
| 3. C2×#17985816 | C2 | semidirect |
| 4. C2×#17985802 | C2 | semidirect |
| 7. C71×#1387 | C2 | semidirect |
| 170. #1387 | D71 | semidirect |
| 171. C71 | #13394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986275 | 2 |
| C2×#17985828 | 2 |
| C2×#17985816 | 2 |
| C2×#17985802 | 2 |
| #22589955 | 2 |
| #22588405 | 2 |
| C71×#1387 | 2 |
| #13394 | 71 |