Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1470 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 469 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. C23×#11924040 | C2 | semidirect |
| 2. C2×C22⋊#11924040 | C2 | direct (N × H) |
| 5. C22×#11924040 | C22 | semidirect |
| 6. C22⋊#11924040 | C22 | direct (N × H) |
| 14. C2×#11924040 | C23 | semidirect |
| 53. C24×C73 | C16 | semidirect |
| 61. C23×C73 | C2×C16 | semidirect |
| 81. C22×C73 | C22⋊C16 | semidirect |
| 84. C22×C73 | C22×C16 | semidirect |
| 93. C2×C73 | C2×C22⋊C16 | semidirect |
| 100. C73 | C22×C22⋊C16 | semidirect |
| 130. C24 | #11924040 | semidirect |
| 158. C23 | C2×#11924040 | semidirect |
| 178. C22 | C22⋊#11924040 | direct (N × H) |
| 181. C22 | C22×#11924040 | semidirect |
| 189. C2 | C2×C22⋊#11924040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924040 | 2 |
| C2×C22⋊#11924040 | 2 |
| C24×#10596833 | 2 |
| C22×C22⋊C16 | 73 |