Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22610105 | C2 | semidirect |
| 3. #22608698 | C2 | semidirect |
| 6. #22607831 | C2 | semidirect |
| 7. C73×#1299 | C2 | semidirect |
| 175. #1299 | D73 | semidirect |
| 176. C73 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619098 | 2 |
| #22610105 | 2 |
| #22608698 | 2 |
| #22608520 | 2 |
| #22608397 | 2 |
| #22607831 | 2 |
| C73×#1299 | 2 |
| #8916 | 73 |