Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 590 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 |
|---|---|---|
| 3. #22624926 | C2 | semidirect |
| 13. #17988506 | C4 | semidirect |
| 18. #17988447 | C4 | semidirect |
| 19. C23×Q8×C73 | C4 | semidirect |
| 172. C73 | #11785 | semidirect |
| 173. C23×Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556649 | 2 |
| #22625190 | 2 |
| #22624926 | 2 |
| #22613290 | 2 |
| #11785 | 73 |