Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #22609548 | C2 | semidirect |
| 5. #22607994 | C2 | semidirect |
| 6. #22607987 | C2 | semidirect |
| 7. C73×#1364 | C2 | semidirect |
| 113. #1364 | D73 | semidirect |
| 114. C73 | #12497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612069 | 2 |
| #22612065 | 2 |
| #22609548 | 2 |
| #22608815 | 2 |
| #22607994 | 2 |
| #22607987 | 2 |
| C73×#1364 | 2 |
| #12497 | 73 |