Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22626964 | C2 | direct (N × H) |
| 67. C22×C4×C73 | C16 | semidirect |
| 80. C2×C4×C73 | C2×C16 | semidirect |
| 125. C2×C73 | #1322 | semidirect |
| 132. C73 | C2×#1322 | semidirect |
| 181. C22×C4 | #11924040 | semidirect |
| 226. C2×C4 | C2×#11924040 | semidirect |
| 253. C2 | #22626964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11924040 | 2 |
| #22626964 | 2 |
| C22×C4⋊#10596833 | 2 |
| C2×#1322 | 73 |