Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22598862 | C2 | semidirect |
| 4. #22586744 | C2 | semidirect |
| 5. #22586743 | C2 | semidirect |
| 6. #22586170 | C2 | semidirect |
| 91. C2×C71⋊C8 | SD16 | semidirect |
| 203. C71 | #10036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598862 | 2 |
| #22598348 | 2 |
| #22589139 | 2 |
| #22586744 | 2 |
| #22586743 | 2 |
| #22586170 | 2 |
| C71×#3101 | 2 |
| #10036 | 71 |