Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1134 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 280 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. C2×#17989506 | C2 | direct (N × H) |
| 11. #17989506 | C22 | direct (N × H) |
| 124. C22×C73 | #362 | semidirect |
| 137. C2×C73 | C2×#362 | semidirect |
| 145. C73 | C22×#362 | semidirect |
| 269. C22 | #17989506 | direct (N × H) |
| 279. C2 | C2×#17989506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556666 | 2 |
| C22×#14556661 | 2 |
| C2×#17989506 | 2 |
| C22×Q16×D73 | 2 |
| C22×#362 | 73 |