Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22588658 | C2 | semidirect |
| 2. C2×#17985733 | C2 | semidirect |
| 3. #22586596 | C2 | semidirect |
| 4. #22586183 | C2 | semidirect |
| 31. C71⋊#95 | D4 | semidirect |
| 232. C71 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588658 | 2 |
| C2×#17985733 | 2 |
| #22586596 | 2 |
| #22586183 | 2 |
| C71×#2656 | 2 |
| #10403 | 71 |