Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
744 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14556510 | C2 | semidirect |
| 4. #22608377 | C2 | semidirect |
| 5. C73×#1467 | C2 | semidirect |
| 200. #1467 | D73 | semidirect |
| 201. C73 | #8368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989310 | 2 |
| C4×#14556510 | 2 |
| #22608530 | 2 |
| #22608377 | 2 |
| C73×#1467 | 2 |
| #8368 | 73 |