Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23755756 | C2 | semidirect |
| 2. #23755755 | C2 | semidirect |
| 3. #23755741 | C2 | semidirect |
| 4. #23755740 | C2 | semidirect |
| 5. #23755737 | C2 | semidirect |
| 6. #23755729 | C2 | semidirect |
| 7. #23755728 | C2 | semidirect |
| 8. C2×#19097305 | C2 | semidirect |
| 9. Q16×D311 | C2 | semidirect |
| 10. #23755716 | C2 | semidirect |
| 11. #137×C311 | C2 | semidirect |
| 87. C311 | #578 | semidirect |
| 94. #137 | D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755756 | 2 |
| #23755755 | 2 |
| #23755741 | 2 |
| #23755740 | 2 |
| #23755737 | 2 |
| #23755729 | 2 |
| #23755728 | 2 |
| C2×#19097305 | 2 |
| Q16×D311 | 2 |
| #23755716 | 2 |
| #137×C311 | 2 |
| #578 | 311 |