Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. #17989512 | C4 | semidirect |
| 15. #17989478 | C4 | semidirect |
| 21. #17988415 | C4 | semidirect |
| 22. #17988414 | C4 | semidirect |
| 23. #17988412 | C4 | semidirect |
| 24. #366×C73 | C4 | semidirect |
| 81. #11924003 | C42 | semidirect |
| 85. C16×C73 | C42 | semidirect |
| 139. C73 | #12677 | semidirect |
| 152. #366 | #64408 | semidirect |
| 217. C16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989512 | 2 |
| C2×#17989478 | 2 |
| #22625746 | 2 |
| #22625738 | 2 |
| #22625005 | 2 |
| #22625002 | 2 |
| #22611716 | 2 |
| #12677 | 73 |