Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 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. #22626332 | C2 | semidirect |
| 2. #22625094 | C2 | semidirect |
| 3. #22625083 | C2 | semidirect |
| 4. C32×#64408 | C2 | semidirect |
| 12. #17988424 | C4 | semidirect |
| 13. D2336 | C4 | semidirect |
| 15. Q64×C73 | C4 | semidirect |
| 68. C73 | #13655 | semidirect |
| 71. Q64 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626332 | 2 |
| #22625094 | 2 |
| #22625083 | 2 |
| C32×#64408 | 2 |
| #22612241 | 2 |
| #13655 | 73 |