Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22586166 | C2 | semidirect |
| 20. C22×Q8×C71 | C8 | semidirect |
| 131. C71 | #7595 | semidirect |
| 146. C22×Q8 | C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588408 | 2 |
| #22586166 | 2 |
| C2×#391×C71 | 2 |
| #7595 | 71 |