Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
410 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 152. C4×C73 | #362 | semidirect |
| 172. C73 | #12819 | semidirect |
| 325. C4 | #17989506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C2×#17989506 | 2 |
| #22625870 | 2 |
| #22625005 | 2 |
| C4×Q16×D73 | 2 |
| #12819 | 73 |