Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 308 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. #22612174 | C2 | semidirect |
| 3. #22609415 | C2 | semidirect |
| 4. #22607983 | C2 | semidirect |
| 5. #22607913 | C2 | semidirect |
| 6. #22607898 | C2 | semidirect |
| 7. C73×#3389 | C2 | semidirect |
| 78. D8×C73 | SD16 | semidirect |
| 146. #3389 | D73 | semidirect |
| 153. C73 | #12360 | semidirect |
| 221. D8 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612174 | 2 |
| #22611966 | 2 |
| #22609415 | 2 |
| #22607983 | 2 |
| #22607913 | 2 |
| #22607898 | 2 |
| C73×#3389 | 2 |
| #12360 | 73 |