Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
214 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 56 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. D16×#64408 | C2 | semidirect |
| 2. #22625092 | C2 | semidirect |
| 3. #22625080 | C2 | semidirect |
| 4. C32×#64408 | C2 | semidirect |
| 12. D2336 | C4 | semidirect |
| 13. #17988422 | C4 | semidirect |
| 15. D32×C73 | C4 | semidirect |
| 23. D1168 | C2×C4 | semidirect |
| 26. #14556497 | C2×C4 | semidirect |
| 27. D16×C73 | C2×C4 | semidirect |
| 28. C32×C73 | C2×C4 | semidirect |
| 61. #64408 | D32 | direct (N × H) |
| 75. C73 | C4×D32 | semidirect |
| 80. D32 | #64408 | direct (N × H) |
| 90. D16 | C2×#64408 | semidirect |
| 98. C32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×#64408 | 2 |
| #22625092 | 2 |
| #22625080 | 2 |
| C32×#64408 | 2 |
| D32×D73 | 2 |
| C4×D32 | 73 |