Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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×#17986056 | C2 | semidirect |
| 3. C2×#17985738 | C2 | semidirect |
| 4. #22586222 | C2 | semidirect |
| 5. C71×#1749 | C2 | semidirect |
| 45. #14556039 | D4 | semidirect |
| 210. #1749 | D71 | semidirect |
| 213. C71 | #9124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986056 | 2 |
| #22596641 | 2 |
| C2×#17985738 | 2 |
| #22586222 | 2 |
| C71×#1749 | 2 |
| #9124 | 71 |