Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22626995 | C2 | direct (N × H) |
| 47. C2×C8×C73 | C16 | semidirect |
| 67. C8×C73 | C2×C16 | semidirect |
| 82. C2×C73 | #1370 | semidirect |
| 89. C73 | C2×#1370 | semidirect |
| 128. C2×C8 | #11924040 | semidirect |
| 154. C8 | C2×#11924040 | semidirect |
| 167. C2 | #22626995 | 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 |
| #22626995 | 2 |
| C2×C8×#10596833 | 2 |
| C2×#1370 | 73 |