Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 120 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. C4×#14556666 | C2 | semidirect |
| 3. C4×#14556661 | C2 | semidirect |
| 4. #22625005 | C2 | semidirect |
| 9. #17989505 | C4 | direct (N × H) |
| 26. #14556666 | C2×C4 | semidirect |
| 29. #14556661 | C2×C4 | semidirect |
| 150. C4×C73 | #361 | semidirect |
| 169. C73 | C4×#361 | semidirect |
| 318. C4 | #17989505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989505 | 2 |
| C4×#14556666 | 2 |
| C4×#14556661 | 2 |
| #22625005 | 2 |
| C4×D8×D73 | 2 |
| C4×#361 | 73 |