Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 93 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. #64408⋊M32 | C2 | semidirect |
| 2. #22627055 | C2 | semidirect |
| 3. #22626977 | C2 | semidirect |
| 8. #64408⋊C16 | C22 | semidirect |
| 9. #17989677 | C22 | semidirect |
| 44. C2×D584 | C8 | semidirect |
| 48. D8×D73 | C8 | semidirect |
| 51. C2×D8×C73 | C8 | semidirect |
| 162. C73 | #11593 | semidirect |
| 186. C2×D8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| #22627055 | 2 |
| #22626977 | 2 |
| C2×D8×#64408 | 2 |
| #11593 | 73 |