Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626757 | C2 | semidirect |
| 2. #22625401 | C2 | semidirect |
| 3. #22625360 | C2 | semidirect |
| 4. #22625343 | C2 | semidirect |
| 5. #22624825 | C2 | semidirect |
| 6. #22624808 | C2 | semidirect |
| 26. #17988996 | C4 | semidirect |
| 27. #17988951 | C4 | semidirect |
| 28. #17988946 | C4 | semidirect |
| 34. #496×C73 | C4 | semidirect |
| 216. C73 | #9432 | semidirect |
| 220. #496 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626757 | 2 |
| #22625401 | 2 |
| #22625360 | 2 |
| #22625343 | 2 |
| #22624825 | 2 |
| #22624808 | 2 |
| #22620626 | 2 |
| #9432 | 73 |