Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
782 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 782 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. #22618972 | C2 | semidirect |
| 2. #22609875 | C2 | semidirect |
| 3. C4×#14556506 | C2 | semidirect |
| 4. #22607817 | C2 | semidirect |
| 17. #395×C73 | C4 | semidirect |
| 19. #394×C73 | C4 | semidirect |
| 20. #393×C73 | C4 | semidirect |
| 22. #392×C73 | C4 | semidirect |
| 26. C2×#11924012 | D4 | semidirect |
| 171. C2×C4×C73 | #104 | semidirect |
| 225. C73 | #9010 | semidirect |
| 235. #395 | Dic73 | semidirect |
| 237. #394 | Dic73 | semidirect |
| 238. #393 | Dic73 | semidirect |
| 240. #392 | Dic73 | semidirect |
| 394. C2×C4 | #14556518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618972 | 2 |
| #22609875 | 2 |
| C4×#14556506 | 2 |
| #22607817 | 2 |
| C73×#2388 | 2 |
| #9010 | 73 |