Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22586399 | C2 | semidirect |
| 5. #22586398 | C2 | semidirect |
| 6. #22586397 | C2 | semidirect |
| 7. C71×#1365 | C2 | semidirect |
| 131. #1365 | D71 | semidirect |
| 132. C71 | #11975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D71 | 2 |
| #22590142 | 2 |
| #22587102 | 2 |
| #22586399 | 2 |
| #22586398 | 2 |
| #22586397 | 2 |
| C71×#1365 | 2 |
| #11975 | 71 |