Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22621133 | C2 | semidirect |
| 5. #22608534 | C2 | semidirect |
| 6. #22607824 | C2 | semidirect |
| 7. C73×#1506 | C2 | semidirect |
| 184. #1506 | D73 | semidirect |
| 186. C73 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621133 | 2 |
| #22620307 | 2 |
| #22615874 | 2 |
| #22608644 | 2 |
| #22608534 | 2 |
| #22607824 | 2 |
| C73×#1506 | 2 |
| #10097 | 73 |