Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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×#64408⋊C16 | C2 | semidirect |
| 2. C2×#17989677 | C2 | semidirect |
| 3. #22626977 | C2 | direct (N × H) |
| 8. #64408⋊C16 | C22 | semidirect |
| 10. #17989677 | C22 | semidirect |
| 44. C2×D584 | C8 | semidirect |
| 48. D8×D73 | C8 | semidirect |
| 51. C2×D8×C73 | C8 | semidirect |
| 83. D584 | C2×C8 | semidirect |
| 93. D8×C73 | C2×C8 | semidirect |
| 157. C2×C73 | #1331 | semidirect |
| 160. D73 | #1331 | semidirect |
| 167. C73 | C2×#1331 | semidirect |
| 191. C2×D8 | #10596842 | semidirect |
| 236. D8 | C2×#10596842 | semidirect |
| 323. C2 | #22626977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64408⋊C16 | 2 |
| C2×#17989677 | 2 |
| #22626977 | 2 |
| C2×D8×#64408 | 2 |
| C2×#1331 | 73 |