Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 2. C2×#17989478 | C2 | semidirect |
| 4. #22624971 | C2 | semidirect |
| 10. #17989482 | C4 | semidirect |
| 11. C22⋊#11924031 | C4 | semidirect |
| 16. C2×#14556530 | C4 | semidirect |
| 17. C2×#14556530 | C4 | semidirect |
| 20. C22×#11924003 | C4 | semidirect |
| 21. C22×C16×C73 | C4 | semidirect |
| 78. #11924003 | C22⋊C4 | semidirect |
| 85. C16×C73 | C22⋊C4 | semidirect |
| 116. C22×C73 | #347 | semidirect |
| 143. C73 | #12616 | semidirect |
| 152. C22×C16 | #64408 | semidirect |
| 223. C16 | C22⋊#64408 | semidirect |
| 261. C22 | #17989478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| C2×#17989478 | 2 |
| #22625667 | 2 |
| #22624971 | 2 |
| C22×#14556530 | 2 |
| #12616 | 73 |