Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
256 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22612068 | C2 | semidirect |
| 3. #22609523 | C2 | semidirect |
| 4. #22607995 | C2 | semidirect |
| 5. #22607987 | C2 | semidirect |
| 6. #22607976 | C2 | semidirect |
| 7. C8×D8×C73 | C2 | semidirect |
| 61. D8×C73 | SD16 | semidirect |
| 94. C8×C73 | D16 | semidirect |
| 120. C8×D8 | D73 | semidirect |
| 124. C73 | #12416 | semidirect |
| 174. D8 | #11924017 | semidirect |
| 211. C8 | #14556532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612068 | 2 |
| #22611966 | 2 |
| #22609523 | 2 |
| #22607995 | 2 |
| #22607987 | 2 |
| #22607976 | 2 |
| C8×D8×C73 | 2 |
| #12416 | 73 |