Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#17986034 | C2 | semidirect |
| 3. C2×#17985810 | C2 | semidirect |
| 4. C2×#17985808 | C2 | semidirect |
| 5. #22589950 | C2 | semidirect |
| 6. #22586445 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 13. #17986241 | C4 | semidirect |
| 14. #17986236 | C4 | semidirect |
| 58. #14556060 | D4 | semidirect |
| 70. #106×C71 | D4 | semidirect |
| 196. #1386 | D71 | semidirect |
| 197. C71 | #13002 | semidirect |
| 258. #106 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597922 | 2 |
| C2×#17986034 | 2 |
| C2×#17985810 | 2 |
| C2×#17985808 | 2 |
| #22589950 | 2 |
| #22586445 | 2 |
| C71×#1386 | 2 |
| #13002 | 71 |