Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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. D16×Dic73 | C2 | semidirect |
| 3. #22611777 | C2 | semidirect |
| 4. #22608130 | C2 | semidirect |
| 5. #22608110 | C2 | semidirect |
| 6. C32×Dic73 | C2 | semidirect |
| 7. C73×#1415 | C2 | semidirect |
| 11. #17988422 | C4 | semidirect |
| 24. D1168 | C2×C4 | semidirect |
| 30. #14556497 | C2×C4 | semidirect |
| 33. D16×C73 | C2×C4 | semidirect |
| 83. Dic73 | D32 | semidirect |
| 95. #1415 | D73 | semidirect |
| 97. C73 | C4×D32 | semidirect |
| 117. D16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988422 | 2 |
| D16×Dic73 | 2 |
| #22611777 | 2 |
| #22608130 | 2 |
| #22608110 | 2 |
| C32×Dic73 | 2 |
| C73×#1415 | 2 |
| C4×D32 | 73 |