Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 2. #22598862 | C2 | semidirect |
| 4. #22586905 | C2 | semidirect |
| 5. #22586904 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 83. C2×C71⋊C8 | SD16 | semidirect |
| 194. C71 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599281 | 2 |
| #22598862 | 2 |
| #22589165 | 2 |
| #22586905 | 2 |
| #22586904 | 2 |
| #22586184 | 2 |
| C71×#3208 | 2 |
| #10220 | 71 |