Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626690 | C2 | semidirect |
| 2. D73⋊#361 | C2 | semidirect |
| 3. #22626240 | C2 | semidirect |
| 4. #22626092 | C2 | semidirect |
| 5. #22624993 | C2 | semidirect |
| 6. #22624984 | C2 | semidirect |
| 22. C2×D1168 | C4 | semidirect |
| 23. C2×#14556532 | C4 | semidirect |
| 24. C2×#14556532 | C4 | semidirect |
| 28. C2×D16×C73 | C4 | semidirect |
| 51. C2×D584 | C2×C4 | semidirect |
| 66. C2×#11924003 | C2×C4 | semidirect |
| 70. C2×D8×C73 | C2×C4 | semidirect |
| 72. C2×C16×C73 | C2×C4 | semidirect |
| 201. C73 | #13017 | semidirect |
| 210. C2×D16 | #64408 | semidirect |
| 238. C2×D8 | C2×#64408 | semidirect |
| 257. C2×C16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626690 | 2 |
| D73⋊#361 | 2 |
| #22626240 | 2 |
| #22626092 | 2 |
| #22624993 | 2 |
| #22624984 | 2 |
| C2×D16×D73 | 2 |
| #13017 | 73 |