Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
690 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×C22⋊#10596842 | C2 | semidirect |
| 2. #22626932 | C2 | semidirect |
| 3. #22626930 | C2 | semidirect |
| 34. C2×#11924029 | C8 | semidirect |
| 36. C2×#11924028 | C8 | semidirect |
| 38. C2×#11924027 | C8 | semidirect |
| 46. C2×#41×C73 | C8 | semidirect |
| 203. C73 | #7563 | semidirect |
| 223. C2×#41 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#10596842 | 2 |
| #22626932 | 2 |
| #22626930 | 2 |
| #22626392 | 2 |
| #7563 | 73 |