Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
| 2. #22609520 | C2 | semidirect |
| 3. D8×#10596831 | C2 | semidirect |
| 4. #22607994 | C2 | semidirect |
| 5. #22607985 | C2 | semidirect |
| 6. #22607977 | C2 | semidirect |
| 65. D8×C73 | SD16 | semidirect |
| 96. #10596831 | D16 | semidirect |
| 124. C73 | #12416 | semidirect |
| 174. D8 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612068 | 2 |
| #22609520 | 2 |
| D8×#10596831 | 2 |
| #22607994 | 2 |
| #22607985 | 2 |
| #22607977 | 2 |
| C73×#2206 | 2 |
| #12416 | 73 |