Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4⋊#11924040 | C2 | semidirect |
| 2. C2×C22⋊#11924040 | C2 | semidirect |
| 3. C2×C4×#11924040 | C2 | semidirect |
| 21. C2×#11924040 | D4 | semidirect |
| 67. C2×D4×C73 | C16 | semidirect |
| 105. C4×C73 | C22⋊C16 | semidirect |
| 122. C73 | #13189 | semidirect |
| 161. C2×D4 | #11924040 | semidirect |
| 228. C4 | C22⋊#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11924040 | 2 |
| C2×C22⋊#11924040 | 2 |
| C2×C4×#11924040 | 2 |
| C2×D4×#10596833 | 2 |
| #13189 | 73 |