Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
844 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C2×#17988374 | C2 | semidirect |
| 2. #22609923 | C2 | semidirect |
| 3. C4×#14556506 | C2 | semidirect |
| 12. C23×D4×C73 | C4 | semidirect |
| 19. #380×C73 | C4 | semidirect |
| 20. #379×C73 | C4 | semidirect |
| 28. #14556506 | D4 | semidirect |
| 194. C4×C73 | AΣL(1,𝔽16) | semidirect |
| 209. C73 | #13221 | semidirect |
| 210. C23×D4 | Dic73 | semidirect |
| 220. #380 | Dic73 | semidirect |
| 221. #379 | Dic73 | semidirect |
| 400. C4 | #17988374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988374 | 2 |
| #22609923 | 2 |
| C4×#14556506 | 2 |
| C73×#2408 | 2 |
| #13221 | 73 |