Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #22624892 | C2 | semidirect |
| 4. #22624891 | C2 | semidirect |
| 32. Q16×D73 | C8 | semidirect |
| 149. C73 | #11600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556666 | 2 |
| #22625479 | 2 |
| #22624892 | 2 |
| #22624891 | 2 |
| C4×Q16×D73 | 2 |
| #11600 | 73 |