Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 3. #22626931 | C2 | semidirect |
| 42. C2×C4⋊Dic73 | C8 | semidirect |
| 46. C4⋊C4×D73 | C8 | semidirect |
| 48. C2×C4⋊C4×C73 | C8 | semidirect |
| 188. C73 | #7593 | semidirect |
| 223. C2×C4⋊C4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627072 | 2 |
| #22626931 | 2 |
| C2×#17989538 | 2 |
| #7593 | 73 |