Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
680 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22626939 | C2 | semidirect |
| 45. C2×C4⋊Dic73 | C8 | semidirect |
| 49. C4⋊C4×D73 | C8 | semidirect |
| 51. C2×C4⋊C4×C73 | C8 | semidirect |
| 197. C73 | #8706 | semidirect |
| 229. C2×C4⋊C4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C4×C22⋊#10596842 | 2 |
| #22626939 | 2 |
| C2×C4⋊C4×#64408 | 2 |
| #8706 | 73 |