Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22586684 | C2 | semidirect |
| 5. C71⋊#1308 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#1491 | C2 | semidirect |
| 198. #1491 | D71 | semidirect |
| 202. C71 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598511 | 2 |
| #22597325 | 2 |
| #22586972 | 2 |
| #22586684 | 2 |
| C71⋊#1308 | 2 |
| #22586212 | 2 |
| C71×#1491 | 2 |
| #9531 | 71 |