Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic146 | C2 | semidirect |
| 2. #22612155 | C2 | semidirect |
| 4. #22609292 | C2 | semidirect |
| 5. #22607987 | C2 | semidirect |
| 6. #22607911 | C2 | semidirect |
| 7. C73×#1331 | C2 | semidirect |
| 78. D8×C73 | SD16 | semidirect |
| 109. Dic146 | D16 | semidirect |
| 143. #1331 | D73 | semidirect |
| 144. C73 | #12352 | semidirect |
| 206. D8 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic146 | 2 |
| #22612155 | 2 |
| #22611966 | 2 |
| #22609292 | 2 |
| #22607987 | 2 |
| #22607911 | 2 |
| C73×#1331 | 2 |
| #12352 | 73 |