Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 5. #17985775 | C4 | semidirect |
| 6. C4×C71⋊C16 | C4 | semidirect |
| 69. C71 | #12593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556068 | 2 |
| #22586420 | 2 |
| C71×#1726 | 2 |
| #12593 | 71 |