Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 237 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. C8×#11924040 | C2 | direct (N × H) |
| 12. C2×#11924040 | C8 | direct (N × H) |
| 26. #11924040 | C2×C8 | direct (N × H) |
| 27. C2×#10596833 | C16 | semidirect |
| 34. C2×#10596831 | C16 | semidirect |
| 41. C2×C8×C73 | C16 | semidirect |
| 55. #10596833 | C2×C16 | semidirect |
| 57. C8×C73 | C2×C16 | semidirect |
| 58. #10596831 | C2×C16 | semidirect |
| 71. C2×C73 | C8×C16 | semidirect |
| 78. C73 | C2×C8×C16 | semidirect |
| 111. C2×C8 | #11924040 | direct (N × H) |
| 133. C8 | C2×#11924040 | direct (N × H) |
| 145. C2 | C8×#11924040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11924040 | 2 |
| C8×#11924040 | 2 |
| C2×C8×#10596833 | 2 |
| C2×C8×C16 | 73 |