Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #22610672 | C2 | semidirect |
| 5. #22608036 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C73×#2159 | C2 | semidirect |
| 19. #17988398 | C4 | semidirect |
| 52. #14556523 | C2×C4 | semidirect |
| 64. M32×C73 | C2×C4 | semidirect |
| 85. Dic292 | C4⋊C4 | semidirect |
| 89. D584 | C4⋊C4 | semidirect |
| 183. #2159 | D73 | semidirect |
| 189. C73 | #12943 | semidirect |
| 236. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618731 | 2 |
| C2×#17988398 | 2 |
| #22611641 | 2 |
| #22610672 | 2 |
| #22608036 | 2 |
| #22608014 | 2 |
| C73×#2159 | 2 |
| #12943 | 73 |