Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22587095 | C2 | semidirect |
| 5. C2×Q8⋊(C71⋊C8) | C2 | semidirect |
| 6. #22586214 | C2 | semidirect |
| 7. C71×#1801 | C2 | semidirect |
| 190. #1801 | D71 | semidirect |
| 196. C71 | #10459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597812 | 2 |
| #22587095 | 2 |
| #22587018 | 2 |
| #22586790 | 2 |
| C2×Q8⋊(C71⋊C8) | 2 |
| #22586214 | 2 |
| C71×#1801 | 2 |
| #10459 | 71 |