Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
782 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 142 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. #22625020 | C2 | semidirect |
| 3. #22625019 | C2 | semidirect |
| 7. #17989567 | C4 | semidirect |
| 11. D73⋊#99 | C4 | semidirect |
| 13. C2×M16×D73 | C4 | semidirect |
| 14. C22×C8×D73 | C4 | semidirect |
| 16. #17988554 | C4 | semidirect |
| 20. #408×C73 | C4 | semidirect |
| 31. #14556649 | C2×C4 | semidirect |
| 46. C2×#11924012 | C2×C4 | semidirect |
| 50. C22×#10596831 | C2×C4 | semidirect |
| 60. C2×M16×C73 | C2×C4 | semidirect |
| 61. C22×C8×C73 | C2×C4 | semidirect |
| 223. D73 | #1391 | semidirect |
| 228. C73 | C2×#1391 | semidirect |
| 243. #408 | #64408 | semidirect |
| 264. C2×M16 | C2×#64408 | semidirect |
| 271. C22×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#410 | 2 |
| #22625020 | 2 |
| #22625019 | 2 |
| #408×D73 | 2 |
| C2×#1391 | 73 |