Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #22586942 | C2 | semidirect |
| 5. #22586209 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 7. C71×#1470 | C2 | semidirect |
| 208. #1470 | D71 | semidirect |
| 211. C71 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986296 | 2 |
| #22597374 | 2 |
| #22586942 | 2 |
| #22586782 | 2 |
| #22586209 | 2 |
| #22586189 | 2 |
| C71×#1470 | 2 |
| #9245 | 71 |