Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#14556062 | C2 | semidirect |
| 3. #22586353 | C2 | semidirect |
| 5. C71×#2163 | C2 | semidirect |
| 7. #17986401 | C4 | semidirect |
| 8. #17986383 | C4 | semidirect |
| 13. C4×Dic284 | C4 | semidirect |
| 15. C4×D568 | C4 | semidirect |
| 149. #2163 | D71 | semidirect |
| 153. C71 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598910 | 2 |
| C4×#14556062 | 2 |
| #22586353 | 2 |
| #22586350 | 2 |
| C71×#2163 | 2 |
| #11746 | 71 |