Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #22593565 | C2 | semidirect |
| 5. #22586218 | C2 | semidirect |
| 6. #22586186 | C2 | semidirect |
| 7. C71×#1289 | C2 | semidirect |
| 228. #1289 | D71 | semidirect |
| 230. C71 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22593565 | 2 |
| #22589175 | 2 |
| #22586907 | 2 |
| C2×#17985734 | 2 |
| #22586218 | 2 |
| #22586186 | 2 |
| C71×#1289 | 2 |
| #10376 | 71 |