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×#17985801 | C2 | semidirect |
| 3. #22588369 | C2 | semidirect |
| 4. C2×C22⋊C16×C71 | C2 | semidirect |
| 9. C22×D568 | C4 | semidirect |
| 11. C2×#14556062 | C22 | semidirect |
| 16. C22×C16×C71 | C22 | semidirect |
| 64. D568 | C22⋊C4 | semidirect |
| 122. C22×C71 | #357 | semidirect |
| 149. C2×C22⋊C16 | D71 | semidirect |
| 151. C71 | #12731 | semidirect |
| 159. C22×C16 | C2×D71 | semidirect |
| 275. C22 | #17985801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D568 | 2 |
| C2×#17985801 | 2 |
| #22588369 | 2 |
| C2×C22⋊C16×C71 | 2 |
| #12731 | 71 |