Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
4830 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 744 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. #22625121 | C2 | direct (N × H) |
| 7. C23×Dic146 | C4 | semidirect |
| 9. C22×Q8×D73 | C4 | semidirect |
| 12. C23×Q8×C73 | C4 | semidirect |
| 15. C23×#64408 | Q8 | semidirect |
| 21. C22×Dic146 | C2×C4 | semidirect |
| 31. C22×Q8×C73 | C2×C4 | semidirect |
| 38. C22×#64408 | C2×Q8 | semidirect |
| 105. C2×C73 | #1446 | semidirect |
| 108. D73 | #1446 | semidirect |
| 114. C73 | C2×#1446 | semidirect |
| 119. C23×Q8 | #64408 | semidirect |
| 132. C22×Q8 | C2×#64408 | semidirect |
| 218. C2 | #22625121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×#64408)⋊C4 | 2 |
| #22625121 | 2 |
| C23×Q8×D73 | 2 |
| C2×#1446 | 73 |