Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2022 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 571 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 |
|---|---|---|
| 1. C22×C4⋊(C71⋊C8) | C2 | semidirect |
| 2. C2×#17985743 | C2 | direct (N × H) |
| 6. C2×C4⋊(C71⋊C8) | C22 | semidirect |
| 7. #17985743 | C22 | direct (N × H) |
| 17. C4⋊(C71⋊C8) | C23 | semidirect |
| 86. C22×C71 | #331 | semidirect |
| 97. C2×C71 | C2×#331 | semidirect |
| 103. C71 | C22×#331 | semidirect |
| 186. C22 | #17985743 | direct (N × H) |
| 196. C2 | C2×#17985743 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C71⋊C8) | 2 |
| C2×#17985743 | 2 |
| C22×#127×C71 | 2 |
| C22×#331 | 71 |