Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
778 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 778 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 |
|---|---|---|
| 2. #22626932 | C2 | direct (N × H) |
| 30. C22×Dic146 | C8 | semidirect |
| 35. C2×Q8×D73 | C8 | semidirect |
| 39. C22×Q8×C73 | C8 | semidirect |
| 64. C2×Dic146 | C2×C8 | semidirect |
| 85. C2×Q8×C73 | C2×C8 | semidirect |
| 156. C2×C73 | #1272 | semidirect |
| 159. D73 | #1272 | semidirect |
| 166. C73 | C2×#1272 | semidirect |
| 185. C22×Q8 | #10596842 | semidirect |
| 218. C2×Q8 | C2×#10596842 | semidirect |
| 322. C2 | #22626932 | 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 |
| #22626932 | 2 |
| C2×(C2×#64408)⋊Q8 | 2 |
| C2×#1272 | 73 |