Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
744 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C4×#14556509 | C2 | semidirect |
| 5. #22608378 | C2 | semidirect |
| 6. #22608274 | C2 | semidirect |
| 7. C73×#1491 | C2 | semidirect |
| 246. #1491 | D73 | semidirect |
| 248. C73 | #8368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989309 | 2 |
| C4×#14556509 | 2 |
| #22608530 | 2 |
| #22608528 | 2 |
| #22608378 | 2 |
| #22608274 | 2 |
| C73×#1491 | 2 |
| #8368 | 73 |