Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22588386 | C2 | semidirect |
| 3. #22586461 | C2 | semidirect |
| 10. C2×#131×C71 | C4 | semidirect |
| 15. #423×C71 | C4 | semidirect |
| 16. #408×C71 | C4 | semidirect |
| 18. C2×C4×C8×C71 | C4 | semidirect |
| 145. C71 | #12807 | semidirect |
| 146. C2×#131 | Dic71 | semidirect |
| 152. #423 | Dic71 | semidirect |
| 154. #408 | Dic71 | semidirect |
| 156. C2×C4×C8 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590005 | 2 |
| #22588386 | 2 |
| #22586461 | 2 |
| C71×#2931 | 2 |
| #12807 | 71 |