Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2334 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1464 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×#14556665 | C2 | direct (N × H) |
| 2. C23×#11924031 | C2 | semidirect |
| 4. C2×#14556665 | C22 | direct (N × H) |
| 5. C22×#11924031 | C22 | semidirect |
| 11. #14556665 | C23 | direct (N × H) |
| 12. C2×#11924031 | C23 | semidirect |
| 23. #11924031 | C24 | semidirect |
| 38. C23×C73 | M32 | semidirect |
| 50. C22×C73 | C2×M32 | semidirect |
| 58. C2×C73 | C22×M32 | semidirect |
| 63. C73 | C23×M32 | semidirect |
| 98. C23 | #14556665 | direct (N × H) |
| 110. C22 | C2×#14556665 | direct (N × H) |
| 117. C2 | C22×#14556665 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556665 | 2 |
| C23×#11924031 | 2 |
| C24×#10596831 | 2 |
| C23×M32 | 73 |