Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 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. #22612218 | C2 | semidirect |
| 3. #22609449 | C2 | semidirect |
| 4. #22607983 | C2 | semidirect |
| 5. #22607913 | C2 | semidirect |
| 74. D8×C73 | Q16 | semidirect |
| 143. C73 | #12414 | semidirect |
| 205. D8 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612218 | 2 |
| #22612078 | 2 |
| #22609449 | 2 |
| #22607983 | 2 |
| #22607913 | 2 |
| #22607898 | 2 |
| C73×#3389 | 2 |
| #12414 | 73 |