Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
410 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. #22590143 | C2 | semidirect |
| 2. #22587096 | C2 | semidirect |
| 3. #22586383 | C2 | semidirect |
| 6. C4⋊(C71⋊C16) | C22 | semidirect |
| 10. #17985750 | C22 | semidirect |
| 138. C71 | #11959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590143 | 2 |
| #22587096 | 2 |
| #22586383 | 2 |
| C2×#495×C71 | 2 |
| #11959 | 71 |