Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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×#14556679 | C2 | direct (N × H) |
| 2. C23×#11924038 | C2 | semidirect |
| 3. C23×#11924036 | C2 | semidirect |
| 5. C2×#14556679 | C22 | direct (N × H) |
| 6. C22×#11924038 | C22 | semidirect |
| 7. C22×#11924036 | C22 | semidirect |
| 15. #14556679 | C23 | direct (N × H) |
| 16. C2×#11924038 | C23 | semidirect |
| 17. C2×#11924036 | C23 | semidirect |
| 29. #11924038 | C24 | semidirect |
| 30. #11924036 | C24 | semidirect |
| 45. C23×C73 | #131 | semidirect |
| 58. C22×C73 | C2×#131 | semidirect |
| 66. C2×C73 | C22×#131 | semidirect |
| 73. C73 | C23×#131 | semidirect |
| 116. C23 | #14556679 | direct (N × H) |
| 129. C22 | C2×#14556679 | direct (N × H) |
| 135. C2 | C22×#14556679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556679 | 2 |
| C23×#11924038 | 2 |
| C23×#11924036 | 2 |
| C23×#11924029 | 2 |
| C23×#131 | 73 |