Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 3. C2×C4×#11924040 | C2 | semidirect |
| 4. #22627001 | C2 | semidirect |
| 7. C22×#11924040 | C4 | semidirect |
| 11. C22⋊#11924040 | C4 | semidirect |
| 43. #11924040 | C22⋊C4 | direct (N × H) |
| 63. C22⋊Dic73 | C16 | semidirect |
| 68. C22⋊C4×C73 | C16 | semidirect |
| 77. C2×C4×C73 | C2×C16 | semidirect |
| 85. C2×Dic73 | C2×C16 | semidirect |
| 99. C22×C73 | C4×C16 | semidirect |
| 123. C73 | C16×C22⋊C4 | semidirect |
| 181. C22⋊C4 | #11924040 | direct (N × H) |
| 207. C2×C4 | C2×#11924040 | semidirect |
| 217. C22 | C4×#11924040 | semidirect |
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 |
| C2×C4×#11924040 | 2 |
| #22627001 | 2 |
| C22⋊C4×#10596833 | 2 |
| C16×C22⋊C4 | 73 |