Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 2. #22599461 | C2 | semidirect |
| 3. #22589330 | C2 | semidirect |
| 4. #22586931 | C2 | semidirect |
| 5. #22586757 | C2 | semidirect |
| 6. #22586230 | C2 | semidirect |
| 7. C71×#3141 | C2 | semidirect |
| 187. #3141 | D71 | semidirect |
| 192. C71 | #10110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599718 | 2 |
| #22599461 | 2 |
| #22589330 | 2 |
| #22586931 | 2 |
| #22586757 | 2 |
| #22586230 | 2 |
| C71×#3141 | 2 |
| #10110 | 71 |