Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22611725 | C2 | semidirect |
| 5. #22608043 | C2 | semidirect |
| 6. #22608042 | C2 | semidirect |
| 7. C73×#2161 | C2 | semidirect |
| 143. #2161 | D73 | semidirect |
| 148. C73 | #12924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988634 | 2 |
| #22611725 | 2 |
| C2×#17988368 | 2 |
| #22609970 | 2 |
| #22608043 | 2 |
| #22608042 | 2 |
| C73×#2161 | 2 |
| #12924 | 73 |