Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22611816 | C2 | semidirect |
| 3. #22611806 | C2 | semidirect |
| 4. #22608120 | C2 | semidirect |
| 5. #22608117 | C2 | semidirect |
| 6. #22608066 | C2 | semidirect |
| 7. C73×#1426 | C2 | semidirect |
| 12. #17988426 | C4 | semidirect |
| 13. D2336 | C4 | semidirect |
| 25. Dic584 | C2×C4 | semidirect |
| 29. D1168 | C2×C4 | semidirect |
| 38. C32×C73 | C2×C4 | semidirect |
| 91. #1426 | D73 | semidirect |
| 95. C73 | #13658 | semidirect |
| 126. C32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612246 | 2 |
| #22611816 | 2 |
| #22611806 | 2 |
| #22608120 | 2 |
| #22608117 | 2 |
| #22608066 | 2 |
| C73×#1426 | 2 |
| #13658 | 73 |