Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22586467 | C2 | semidirect |
| 4. #22586466 | C2 | semidirect |
| 5. C71×#1394 | C2 | semidirect |
| 11. #17985982 | C4 | semidirect |
| 46. #14556047 | C2×C4 | semidirect |
| 54. #101×C71 | C2×C4 | semidirect |
| 194. #1394 | D71 | semidirect |
| 195. C71 | #12587 | semidirect |
| 242. #101 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985982 | 2 |
| #22590931 | 2 |
| #22586467 | 2 |
| #22586466 | 2 |
| C71×#1394 | 2 |
| #12587 | 71 |