Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
726 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 192 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. #22626656 | C2 | semidirect |
| 2. #22625531 | C2 | semidirect |
| 3. #22625490 | C2 | semidirect |
| 4. #22625278 | C2 | semidirect |
| 5. #22625127 | C2 | semidirect |
| 62. #11924036 | D8 | semidirect |
| 143. C73 | #17975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626656 | 2 |
| #22625531 | 2 |
| #22625490 | 2 |
| #22625278 | 2 |
| #22625127 | 2 |
| #22620511 | 2 |
| #17975 | 73 |