Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 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. #22612167 | C2 | semidirect |
| 2. #22612078 | C2 | semidirect |
| 3. #22609444 | C2 | semidirect |
| 4. #22607974 | C2 | semidirect |
| 5. #22607898 | C2 | semidirect |
| 6. #22607889 | C2 | semidirect |
| 8. #17988992 | C22 | semidirect |
| 11. C4⋊#11924003 | C22 | semidirect |
| 15. #17988363 | C22 | semidirect |
| 16. #17988338 | C22 | semidirect |
| 91. D8×C73 | SD16 | semidirect |
| 174. C73 | #12378 | semidirect |
| 253. D8 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612167 | 2 |
| #22612078 | 2 |
| #22609444 | 2 |
| #22607974 | 2 |
| #22607898 | 2 |
| #22607889 | 2 |
| C73×#3273 | 2 |
| #12378 | 73 |