Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 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. #22588471 | C2 | semidirect |
| 4. #22586199 | C2 | semidirect |
| 5. C71×#1564 | C2 | semidirect |
| 9. #17986078 | C4 | semidirect |
| 11. C8×D284 | C4 | semidirect |
| 137. #1564 | D71 | semidirect |
| 140. C71 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597053 | 2 |
| #22588471 | 2 |
| #22586901 | 2 |
| #22586199 | 2 |
| C71×#1564 | 2 |
| #8680 | 71 |