Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22626808 | C2 | semidirect |
| 2. #22625356 | C2 | semidirect |
| 3. #22625336 | C2 | semidirect |
| 4. #22625206 | C2 | semidirect |
| 5. #22624835 | C2 | semidirect |
| 6. #22624802 | C2 | semidirect |
| 26. #17988918 | C4 | semidirect |
| 28. #17988898 | C4 | semidirect |
| 31. #17988738 | C4 | semidirect |
| 34. #447×C73 | C4 | semidirect |
| 233. C73 | #9332 | semidirect |
| 243. #447 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626808 | 2 |
| #22625356 | 2 |
| #22625336 | 2 |
| #22625206 | 2 |
| #22624835 | 2 |
| #22624802 | 2 |
| #22620742 | 2 |
| #9332 | 73 |