Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1390 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1390 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 |
|---|---|---|
| 1. C22×#14556666 | C2 | semidirect |
| 2. C22×#14556661 | C2 | semidirect |
| 3. C2×#17989505 | C2 | direct (N × H) |
| 7. C2×#14556666 | C22 | semidirect |
| 10. C2×#14556661 | C22 | semidirect |
| 11. #17989505 | C22 | direct (N × H) |
| 25. #14556666 | C23 | semidirect |
| 28. #14556661 | C23 | semidirect |
| 131. C22×C73 | #361 | semidirect |
| 147. C2×C73 | C2×#361 | semidirect |
| 156. C73 | C22×#361 | semidirect |
| 291. C22 | #17989505 | direct (N × H) |
| 301. C2 | C2×#17989505 | 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×#17989505 | 2 |
| C22×D8×D73 | 2 |
| C22×#361 | 73 |