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. #23755740 | C2 | semidirect |
| 3. #23755739 | C2 | semidirect |
| 4. #23755731 | C2 | semidirect |
| 5. #23755730 | C2 | semidirect |
| 6. Q16×D311 | C2 | semidirect |
| 7. #23755714 | C2 | semidirect |
| 8. C2×Q16×C311 | C2 | semidirect |
| 59. C311 | #578 | semidirect |
| 67. C2×Q16 | D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755756 | 2 |
| #23755740 | 2 |
| #23755739 | 2 |
| #23755731 | 2 |
| #23755730 | 2 |
| Q16×D311 | 2 |
| #23755714 | 2 |
| C2×Q16×C311 | 2 |
| #578 | 311 |