Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22608323 | C2 | semidirect |
| 3. #22608251 | C2 | semidirect |
| 4. #22608223 | C2 | semidirect |
| 5. C73×#1564 | C2 | semidirect |
| 143. #1564 | D73 | semidirect |
| 147. C73 | #9670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D584 | 2 |
| #22608323 | 2 |
| #22608251 | 2 |
| #22608223 | 2 |
| C73×#1564 | 2 |
| #9670 | 73 |