Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
506 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #22627040 | C2 | semidirect |
| 3. #22626941 | C2 | semidirect |
| 22. C2×#11924038 | C8 | semidirect |
| 25. C2×#11924037 | C8 | semidirect |
| 41. C22×#10596831 | C8 | semidirect |
| 46. C2×C8×D73 | C8 | semidirect |
| 47. C2×C8×D73 | C8 | semidirect |
| 50. C22×C8×C73 | C8 | semidirect |
| 163. C73 | #8156 | semidirect |
| 194. C22×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627043 | 2 |
| #22627040 | 2 |
| #22626941 | 2 |
| C2×#17989550 | 2 |
| #8156 | 73 |