Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
572 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 1. #22598458 | C2 | semidirect |
| 2. #22593829 | C2 | semidirect |
| 3. #22589260 | C2 | semidirect |
| 4. #22586938 | C2 | semidirect |
| 5. #22586786 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 224. C71 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598458 | 2 |
| #22593829 | 2 |
| #22589260 | 2 |
| #22586938 | 2 |
| #22586786 | 2 |
| #22586197 | 2 |
| C71×#3213 | 2 |
| #10006 | 71 |