Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
682 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 682 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 |
|---|---|---|
| 1. C2×C22⋊#11924040 | C2 | semidirect |
| 2. #22626952 | C2 | direct (N × H) |
| 6. C22⋊#11924040 | C22 | semidirect |
| 79. C24×C73 | C16 | semidirect |
| 99. C23×C73 | C2×C16 | semidirect |
| 158. C2×C73 | #1314 | semidirect |
| 165. C73 | C2×#1314 | semidirect |
| 205. C24 | #11924040 | semidirect |
| 261. C23 | C2×#11924040 | semidirect |
| 319. C2 | #22626952 | 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 |
| #22626952 | 2 |
| C22×C22⋊#10596833 | 2 |
| C2×#1314 | 73 |