Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22627062 | C2 | semidirect |
| 2. #22626991 | C2 | semidirect |
| 3. #22626979 | C2 | semidirect |
| 4. #22626950 | C2 | semidirect |
| 27. D1168 | C8 | semidirect |
| 28. #14556532 | C8 | semidirect |
| 30. D16×C73 | C8 | semidirect |
| 42. D584 | C2×C8 | semidirect |
| 45. #11924003 | C2×C8 | semidirect |
| 46. D8×C73 | C2×C8 | semidirect |
| 47. C16×C73 | C2×C8 | semidirect |
| 81. C73 | #12067 | semidirect |
| 97. D16 | #10596842 | semidirect |
| 111. D8 | C2×#10596842 | semidirect |
| 123. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627062 | 2 |
| #22626991 | 2 |
| #22626979 | 2 |
| #22626950 | 2 |
| #22626329 | 2 |
| #12067 | 73 |