Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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×#17988398 | C2 | semidirect |
| 3. #22611641 | C2 | semidirect |
| 4. C2×#17988368 | C2 | semidirect |
| 5. #22609965 | C2 | semidirect |
| 6. #22608036 | C2 | semidirect |
| 7. C73×#2159 | C2 | semidirect |
| 69. M32×C73 | D4 | semidirect |
| 209. #2159 | D73 | semidirect |
| 215. C73 | #13386 | semidirect |
| 269. M32 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619541 | 2 |
| C2×#17988398 | 2 |
| #22611641 | 2 |
| C2×#17988368 | 2 |
| #22609965 | 2 |
| #22608036 | 2 |
| C73×#2159 | 2 |
| #13386 | 73 |