Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22612079 | C2 | semidirect |
| 3. #22609523 | C2 | semidirect |
| 4. C8×D584 | C2 | semidirect |
| 5. #22607988 | C2 | semidirect |
| 6. #22607978 | C2 | semidirect |
| 7. C73×#1367 | C2 | semidirect |
| 56. D584 | SD16 | semidirect |
| 119. #1367 | D73 | semidirect |
| 122. C73 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612079 | 2 |
| #22611967 | 2 |
| #22609523 | 2 |
| C8×D584 | 2 |
| #22607988 | 2 |
| #22607978 | 2 |
| C73×#1367 | 2 |
| #12418 | 73 |