Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1162 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 291 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. #22627174 | C2 | semidirect |
| 2. #22627046 | C2 | semidirect |
| 35. C22×Dic146 | C8 | semidirect |
| 38. C2×Q8×D73 | C8 | semidirect |
| 39. C2×Q8×D73 | C8 | semidirect |
| 43. C22×Q8×C73 | C8 | semidirect |
| 145. C73 | #17352 | semidirect |
| 165. C22×Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627174 | 2 |
| #22627046 | 2 |
| #22627043 | 2 |
| C2×#17989655 | 2 |
| #17352 | 73 |