Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
194 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 50 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. #22626335 | C2 | semidirect |
| 2. #22626329 | C2 | semidirect |
| 3. #22625097 | C2 | semidirect |
| 4. #22625086 | C2 | semidirect |
| 5. #22625084 | C2 | semidirect |
| 6. #22625041 | C2 | semidirect |
| 18. #17988426 | C4 | semidirect |
| 19. #17988425 | C4 | semidirect |
| 20. #17988422 | C4 | semidirect |
| 22. D32×C73 | C4 | semidirect |
| 34. Dic584 | C2×C4 | semidirect |
| 39. #14556497 | C2×C4 | semidirect |
| 41. D16×C73 | C2×C4 | semidirect |
| 42. C32×C73 | C2×C4 | semidirect |
| 103. C73 | #13658 | semidirect |
| 111. D32 | #64408 | semidirect |
| 128. D16 | C2×#64408 | semidirect |
| 138. C32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626335 | 2 |
| #22626329 | 2 |
| #22625097 | 2 |
| #22625086 | 2 |
| #22625084 | 2 |
| #22625041 | 2 |
| #22612242 | 2 |
| #13658 | 73 |