Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609923 | C2 | semidirect |
| 3. #22608690 | C2 | semidirect |
| 4. #22608606 | C2 | semidirect |
| 5. #22608383 | C2 | semidirect |
| 6. #22607806 | C2 | semidirect |
| 7. C2×D4⋊C8×C73 | C2 | semidirect |
| 206. C2×D4⋊C8 | D73 | semidirect |
| 208. C73 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619395 | 2 |
| #22609923 | 2 |
| #22608690 | 2 |
| #22608606 | 2 |
| #22608383 | 2 |
| #22607806 | 2 |
| C2×D4⋊C8×C73 | 2 |
| #10456 | 73 |