Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #22597191 | C2 | semidirect |
| 3. C2×#17985811 | C2 | semidirect |
| 4. #22590055 | C2 | semidirect |
| 5. #22589248 | C2 | semidirect |
| 6. #22586428 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 13. C2×D1136 | C4 | semidirect |
| 37. C2×D568 | C2×C4 | semidirect |
| 59. C2×C16×C71 | C2×C4 | semidirect |
| 171. #1382 | D71 | semidirect |
| 173. C71 | #13017 | semidirect |
| 220. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| #22597191 | 2 |
| C2×#17985811 | 2 |
| #22590055 | 2 |
| #22589248 | 2 |
| #22586428 | 2 |
| C71×#1382 | 2 |
| #13017 | 71 |