Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22588497 | C2 | semidirect |
| 3. #22588467 | C2 | semidirect |
| 4. C71⋊#1273 | C2 | semidirect |
| 114. C71 | #10677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589147 | 2 |
| #22588497 | 2 |
| #22588467 | 2 |
| C71⋊#1273 | 2 |
| C71×#1957 | 2 |
| #10677 | 71 |