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. #22610106 | C2 | semidirect |
| 3. #22608699 | C2 | semidirect |
| 6. #22607822 | C2 | semidirect |
| 7. C73×#1302 | C2 | semidirect |
| 174. #1302 | 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 |
|---|---|
| #22619103 | 2 |
| #22610106 | 2 |
| #22608699 | 2 |
| #22608517 | 2 |
| #22608397 | 2 |
| #22607822 | 2 |
| C73×#1302 | 2 |
| #8916 | 73 |