Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22627019 | C2 | direct (N × H) |
| 4. #17989695 | C4 | semidirect |
| 6. C2×#14556681 | C4 | semidirect |
| 12. #14556681 | C2×C4 | semidirect |
| 67. C2×C73 | #1398 | semidirect |
| 72. C73 | C2×#1398 | semidirect |
| 135. C2 | #22627019 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989695 | 2 |
| #22627019 | 2 |
| C2×#17989475 | 2 |
| C2×#1398 | 73 |