Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#17985836 | C2 | semidirect |
| 3. C4×D1136 | C2 | semidirect |
| 4. C4⋊(C71⋊C32) | C2 | semidirect |
| 5. #22586521 | C2 | semidirect |
| 6. #22586518 | C2 | semidirect |
| 7. C71×#2249 | C2 | semidirect |
| 100. #2249 | D71 | semidirect |
| 105. C71 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985836 | 2 |
| C2×#17985834 | 2 |
| C4×D1136 | 2 |
| C4⋊(C71⋊C32) | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C71×#2249 | 2 |
| #13689 | 71 |