Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611963 | C2 | semidirect |
| 2. C8×D584 | C2 | semidirect |
| 3. #22608001 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 5. C73×#1712 | C2 | semidirect |
| 38. D584 | D8 | semidirect |
| 77. C8×C73 | D16 | semidirect |
| 101. #1712 | D73 | semidirect |
| 105. C73 | #12424 | semidirect |
| 178. C8 | #14556532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611963 | 2 |
| C8×D584 | 2 |
| #22608001 | 2 |
| #22607977 | 2 |
| C73×#1712 | 2 |
| #12424 | 73 |