Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
494 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 108 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. #22626261 | C2 | semidirect |
| 3. #22625868 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 15. C4×D584 | C4 | semidirect |
| 16. D8×Dic73 | C4 | semidirect |
| 17. #17988669 | C4 | semidirect |
| 23. C4×D8×C73 | C4 | semidirect |
| 190. C73 | #12813 | semidirect |
| 199. C4×D8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626261 | 2 |
| C2×#17989499 | 2 |
| #22625868 | 2 |
| #22624988 | 2 |
| C4×D8×D73 | 2 |
| #12813 | 73 |