Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. #22620491 | C2 | semidirect |
| 3. #22609533 | C2 | semidirect |
| 4. #22609529 | C2 | semidirect |
| 5. #22609524 | C2 | semidirect |
| 6. #22609519 | C2 | semidirect |
| 7. C2×C8×#10596831 | C2 | semidirect |
| 8. C73×#3160 | C2 | semidirect |
| 79. C2×C8×C73 | SD16 | semidirect |
| 109. #10596831 | #135 | semidirect |
| 127. #3160 | D73 | semidirect |
| 134. C73 | #19596 | semidirect |
| 203. C2×C8 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620491 | 2 |
| #22620359 | 2 |
| #22609533 | 2 |
| #22609529 | 2 |
| #22609524 | 2 |
| #22609519 | 2 |
| C2×C8×#10596831 | 2 |
| C73×#3160 | 2 |
| #19596 | 73 |