Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #22608105 | C2 | direct (N × H) |
| 5. C2×#14556583 | C4 | semidirect |
| 8. #17988941 | C4 | semidirect |
| 13. C2×C4×#10596831 | C4 | semidirect |
| 24. #14556583 | C2×C4 | semidirect |
| 34. C4×#10596831 | C2×C4 | semidirect |
| 134. C2×C73 | #1414 | semidirect |
| 140. C73 | C2×#1414 | semidirect |
| 269. C2 | #22608105 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988941 | 2 |
| C2×#17988384 | 2 |
| #22608105 | 2 |
| C2×#354×C73 | 2 |
| C2×#1414 | 73 |