Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17985799 | C2 | semidirect |
| 3. C2×C22⋊(C71⋊C16) | C2 | semidirect |
| 4. C71×#1808 | C2 | semidirect |
| 9. C22×D568 | C4 | semidirect |
| 11. C22×C71⋊C16 | C22 | semidirect |
| 15. C2×#107×C71 | C22 | semidirect |
| 63. D568 | C22⋊C4 | semidirect |
| 122. C22×C71 | #357 | semidirect |
| 150. #1808 | D71 | semidirect |
| 151. C71 | #12731 | semidirect |
| 160. C2×#107 | C2×D71 | semidirect |
| 275. C22 | #17985799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D568 | 2 |
| C2×#17985799 | 2 |
| C2×C22⋊(C71⋊C16) | 2 |
| C71×#1808 | 2 |
| #12731 | 71 |