Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 37. #14556591 | C8 | semidirect |
| 39. #14556589 | C8 | semidirect |
| 40. #14556589 | C8 | semidirect |
| 43. C4⋊Q8×C73 | C8 | semidirect |
| 143. C73 | #11482 | semidirect |
| 162. C4⋊Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627046 | 2 |
| #22626967 | 2 |
| #22626959 | 2 |
| #22626422 | 2 |
| #11482 | 73 |