Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590535 | C2 | semidirect |
| 2. #22590523 | C2 | semidirect |
| 3. #22589780 | C2 | semidirect |
| 4. #22586358 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586266 | C2 | semidirect |
| 164. C71 | #12285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590535 | 2 |
| #22590523 | 2 |
| #22589780 | 2 |
| #22586358 | 2 |
| #22586355 | 2 |
| #22586266 | 2 |
| C71×#3203 | 2 |
| #12285 | 71 |