Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1022 conjugacy classes of subgroups; only the 629 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 629 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. C2×C4×#11924040 | C2 | direct (N × H) |
| 4. C22×#11924040 | C4 | direct (N × H) |
| 6. C4×#11924040 | C22 | direct (N × H) |
| 12. C2×#11924040 | C2×C4 | direct (N × H) |
| 26. #11924040 | C22×C4 | direct (N × H) |
| 33. C22×Dic73 | C16 | semidirect |
| 42. C22×C4×C73 | C16 | semidirect |
| 48. C2×C4×C73 | C2×C16 | semidirect |
| 51. C2×Dic73 | C2×C16 | semidirect |
| 60. C22×C73 | C4×C16 | semidirect |
| 65. C4×C73 | C22×C16 | semidirect |
| 67. Dic73 | C22×C16 | semidirect |
| 71. C2×C73 | C2×C4×C16 | semidirect |
| 78. C73 | C22×C4×C16 | semidirect |
| 108. C22×C4 | #11924040 | direct (N × H) |
| 130. C2×C4 | C2×#11924040 | direct (N × H) |
| 135. C22 | C4×#11924040 | direct (N × H) |
| 144. C4 | C22×#11924040 | direct (N × H) |
| 145. C2 | C2×C4×#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×C4×#11924040 | 2 |
| C22×C4×#10596833 | 2 |
| C22×C4×C16 | 73 |