Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17988386 | C2 | semidirect |
| 3. #22608097 | C2 | direct (N × H) |
| 4. C2×#356×C73 | C2 | semidirect |
| 15. #17988386 | C22 | semidirect |
| 19. #356×C73 | C22 | semidirect |
| 149. C2×C73 | #1410 | semidirect |
| 154. C2×#356 | D73 | semidirect |
| 156. C73 | C2×#1410 | semidirect |
| 171. #356 | C2×D73 | semidirect |
| 301. C2 | #22608097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988961 | 2 |
| C2×#17988386 | 2 |
| #22608097 | 2 |
| C2×#356×C73 | 2 |
| C2×#1410 | 73 |