Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
982 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 411 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. C71⋊#1273 | C2 | semidirect |
| 3. C71×#1273 | C2 | semidirect |
| 14. C2×C8×D71 | C8 | semidirect |
| 31. C2×C71⋊C8 | C2×C8 | semidirect |
| 38. C2×C8×C71 | C2×C8 | semidirect |
| 69. D71 | #1273 | direct (N × H) |
| 72. #1273 | D71 | direct (N × H) |
| 73. C71 | C2×#1273 | semidirect |
| 106. C2×C8 | C8×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×D71 | 2 |
| C71⋊#1273 | 2 |
| C71×#1273 | 2 |
| C2×#1273 | 71 |