Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22618521 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22608033 | C2 | semidirect |
| 5. C2×#349×C73 | C2 | semidirect |
| 9. #17988845 | C4 | semidirect |
| 10. #17988840 | C4 | semidirect |
| 24. C2×Dic292 | C2×C4 | semidirect |
| 26. C2×D584 | C2×C4 | semidirect |
| 44. #14556523 | C2×C4 | semidirect |
| 45. #14556523 | D4 | semidirect |
| 165. C2×#349 | D73 | semidirect |
| 167. C73 | #13008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619540 | 2 |
| #22618521 | 2 |
| #22611668 | 2 |
| #22608033 | 2 |
| C2×#349×C73 | 2 |
| #13008 | 73 |