Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22588460 | C2 | semidirect |
| 3. #22587036 | C2 | semidirect |
| 4. #22587035 | C2 | semidirect |
| 5. #22586847 | C2 | semidirect |
| 6. #22586209 | C2 | semidirect |
| 7. C71×#1505 | C2 | semidirect |
| 170. #1505 | D71 | semidirect |
| 172. C71 | #10513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599647 | 2 |
| #22588460 | 2 |
| #22587036 | 2 |
| #22587035 | 2 |
| #22586847 | 2 |
| #22586209 | 2 |
| C71×#1505 | 2 |
| #10513 | 71 |