Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
4126 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2232 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. C22×#14556646 | C2 | direct (N × H) |
| 4. C23×#10596833 | C4 | semidirect |
| 6. C2×#14556646 | C22 | direct (N × H) |
| 12. C22×#10596833 | C2×C4 | semidirect |
| 14. #14556646 | C23 | direct (N × H) |
| 25. C2×#10596833 | C22×C4 | semidirect |
| 41. C23×C73 | #97 | semidirect |
| 54. #10596833 | C23×C4 | semidirect |
| 55. C22×C73 | C2×#97 | semidirect |
| 65. C2×C73 | C22×#97 | semidirect |
| 72. C73 | C23×#97 | semidirect |
| 110. C23 | #14556646 | direct (N × H) |
| 124. C22 | C2×#14556646 | direct (N × H) |
| 133. C2 | C22×#14556646 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596833 | 2 |
| C22×#14556646 | 2 |
| C23×C4×Dic73 | 2 |
| C23×#97 | 73 |