Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
572 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 205 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. #22627146 | C2 | semidirect |
| 2. #22627140 | C2 | semidirect |
| 3. #22627131 | C2 | semidirect |
| 4. #22627103 | C2 | semidirect |
| 111. C73 | #33493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627146 | 2 |
| #22627140 | 2 |
| #22627131 | 2 |
| #22627103 | 2 |
| #22626656 | 2 |
| #33493 | 73 |