Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22588336 | C2 | semidirect |
| 3. #22587099 | C2 | semidirect |
| 6. #22586215 | C2 | semidirect |
| 7. C2×Q8⋊C8×C71 | C2 | semidirect |
| 194. C2×Q8⋊C8 | D71 | semidirect |
| 196. C71 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597812 | 2 |
| #22588336 | 2 |
| #22587099 | 2 |
| #22587015 | 2 |
| #22586792 | 2 |
| #22586215 | 2 |
| C2×Q8⋊C8×C71 | 2 |
| #10458 | 71 |