Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
594 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626119 | C2 | semidirect |
| 4. #22625363 | C2 | semidirect |
| 5. #22624785 | C2 | semidirect |
| 6. #22624754 | C2 | semidirect |
| 22. #17988961 | C4 | semidirect |
| 23. #17988934 | C4 | semidirect |
| 24. #17988933 | C4 | semidirect |
| 28. #492×C73 | C4 | semidirect |
| 52. #14556591 | C2×C4 | semidirect |
| 68. C4×#10596831 | C2×C4 | semidirect |
| 70. C4⋊Q8×C73 | C2×C4 | semidirect |
| 72. C4×C8×C73 | C2×C4 | semidirect |
| 91. C4×#64408 | SD16 | semidirect |
| 223. C73 | #9295 | semidirect |
| 228. #492 | #64408 | semidirect |
| 253. C4⋊Q8 | C2×#64408 | semidirect |
| 284. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626423 | 2 |
| #22626119 | 2 |
| #22625439 | 2 |
| #22625363 | 2 |
| #22624785 | 2 |
| #22624754 | 2 |
| #22620868 | 2 |
| #9295 | 73 |