Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22597446 | C2 | semidirect |
| 5. C71⋊#1308 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#1554 | C2 | semidirect |
| 156. #1554 | D71 | semidirect |
| 161. C71 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599339 | 2 |
| #22597446 | 2 |
| #22586963 | 2 |
| #22586691 | 2 |
| C71⋊#1308 | 2 |
| #22586202 | 2 |
| C71×#1554 | 2 |
| #9334 | 71 |