Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. C19×H(5,𝔽2) | C2 | semidirect |
| 2. #10597436 | C2 | semidirect |
| 3. #10597397 | C2 | semidirect |
| 4. #10597396 | C2 | semidirect |
| 5. #10597394 | C2 | semidirect |
| 6. C2×#64526 | C2 | semidirect |
| 7. #10597378 | C2 | semidirect |
| 15. #64541 | C22 | semidirect |
| 16. C2×Dic38 | C22 | semidirect |
| 17. #64528 | C22 | semidirect |
| 18. #64527 | C22 | semidirect |
| 19. #64526 | C22 | semidirect |
| 20. #64526 | C22 | semidirect |
| 21. #64525 | C22 | semidirect |
| 22. #64520 | C22 | semidirect |
| 23. C2×C19⋊C8 | C22 | semidirect |
| 55. H(5,𝔽2) | D19 | semidirect |
| 61. C19 | #577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×H(5,𝔽2) | 2 |
| #10597436 | 2 |
| #10597397 | 2 |
| #10597396 | 2 |
| #10597394 | 2 |
| C2×#64526 | 2 |
| #10597378 | 2 |
| #577 | 19 |