Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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×(C2×#10596842)⋊C4 | C2 | semidirect |
| 2. #22626930 | C2 | direct (N × H) |
| 6. (C2×#10596842)⋊C4 | C22 | semidirect |
| 32. C22×D292 | C8 | semidirect |
| 38. C2×D4×D73 | C8 | semidirect |
| 41. C22×D4×C73 | C8 | semidirect |
| 73. C2×D292 | C2×C8 | semidirect |
| 93. C2×D4×C73 | C2×C8 | semidirect |
| 180. C2×C73 | #1270 | semidirect |
| 184. D73 | #1270 | semidirect |
| 191. C73 | C2×#1270 | semidirect |
| 211. C22×D4 | #10596842 | semidirect |
| 253. C2×D4 | C2×#10596842 | semidirect |
| 372. C2 | #22626930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626930 | 2 |
| C2×#17989539 | 2 |
| C2×#1270 | 73 |